%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA146-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:53 PM UTC 2026
% Result : Unsatisfiable 1.54s 1.75s
% Output : Proof 3.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA146-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.14/0.32 % Computer : n006.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:35:02 EDT 2026
% 0.14/0.32 % CPUTime :
% 1.54/1.75 % SZS status Unsatisfiable
% 1.54/1.75 % SZS output start Proof
% 1.54/1.75 tff(r_type, type, (
% 1.54/1.75 r: ( $i * $i ) > $o)).
% 1.54/1.75 tff(s_type, type, (
% 1.54/1.75 s: $i > $i)).
% 1.54/1.75 tff(z_type, type, (
% 1.54/1.75 z: $i)).
% 1.54/1.75 tff(b_type, type, (
% 1.54/1.75 b: ( $i * $i ) > $o)).
% 1.54/1.75 tff(inj_0_type, type, (
% 1.54/1.75 inj_0: $i > $i)).
% 1.54/1.75 tff(elem_1_type, type, (
% 1.54/1.75 elem_1: $i)).
% 1.54/1.75 tff(1,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.54/1.75 tff(2,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.54/1.75 tff(3,assumption,(r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(4,assumption,(b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.54/1.75 tff(5,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.54/1.75 tff(6,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.54/1.75 tff(7,plain,
% 1.54/1.75 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(8,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[7])).
% 1.54/1.75 tff(9,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(10,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 1.54/1.75 tff(11,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[10, 9])).
% 1.54/1.75 tff(12,plain,(
% 1.54/1.75 ![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(skolemize,[status(sab)],[11])).
% 1.54/1.75 tff(13,plain,
% 1.54/1.75 (![X: $i] : (~(s(X) = z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.54/1.75 tff(14,plain,
% 1.54/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(15,plain,
% 1.54/1.75 (~(s(z) = z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[14, 13])).
% 1.54/1.75 tff(16,plain,
% 1.54/1.75 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(17,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[16])).
% 1.54/1.75 tff(18,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(19,plain,
% 1.54/1.75 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(20,plain,
% 1.54/1.75 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[19])).
% 1.54/1.75 tff(21,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 1.54/1.75 tff(22,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[21, 20])).
% 1.54/1.75 tff(23,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[22, 18])).
% 1.54/1.75 tff(24,plain,(
% 1.54/1.75 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(skolemize,[status(sab)],[23])).
% 1.54/1.75 tff(25,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[24, 17])).
% 1.54/1.75 tff(26,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(27,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(28,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[27, 26])).
% 1.54/1.75 tff(29,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[28, 25, 15, 6, 5])).
% 1.54/1.75 tff(30,plain,(b(s(z), z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(31,plain,
% 1.54/1.75 (r(s(z), z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[30, 5])).
% 1.54/1.75 tff(32,assumption,(~b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.75 tff(33,plain,
% 1.54/1.75 ((s(s(s(s(s(z))))) = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(34,plain,
% 1.54/1.75 ((~(s(s(s(s(s(z))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[33])).
% 1.54/1.75 tff(35,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(36,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(37,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(38,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 1.54/1.75 tff(39,plain,
% 1.54/1.75 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.54/1.75 tff(40,plain,(
% 1.54/1.75 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.54/1.75 inference(skolemize,[status(sab)],[39])).
% 1.54/1.75 tff(41,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[40, 36])).
% 1.54/1.75 tff(42,plain,
% 1.54/1.75 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[41, 35])).
% 1.54/1.75 tff(43,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(44,plain,
% 1.54/1.75 (inj_0(s(z)) = z),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[43, 42])).
% 1.54/1.75 tff(45,assumption,(s(s(s(s(s(z))))) = s(z)), introduced(assumption)).
% 1.54/1.75 tff(46,plain,
% 1.54/1.75 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[45])).
% 1.54/1.75 tff(47,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(48,plain,
% 1.54/1.75 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[47, 42])).
% 1.54/1.75 tff(49,plain,
% 1.54/1.75 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.75 inference(symmetry,[status(thm)],[48])).
% 1.54/1.75 tff(50,plain,
% 1.54/1.75 (s(s(s(s(z)))) = z),
% 1.54/1.75 inference(transitivity,[status(thm)],[49, 46, 44])).
% 1.54/1.75 tff(51,plain,
% 1.54/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(52,plain,
% 1.54/1.75 (~(s(s(s(s(z)))) = z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[51, 13])).
% 1.54/1.75 tff(53,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[52, 50])).
% 1.54/1.75 tff(54,plain,(~(s(s(s(s(s(z))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(55,plain,
% 1.54/1.75 (~(s(z) = s(s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[54, 34])).
% 1.54/1.75 tff(56,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(57,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(58,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[57, 56])).
% 1.54/1.75 tff(59,plain,
% 1.54/1.75 ((s(z) = s(s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[58, 25])).
% 1.54/1.75 tff(60,plain,
% 1.54/1.75 (b(s(z), s(s(s(s(s(z)))))) | r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[59, 55])).
% 1.54/1.75 tff(61,plain,
% 1.54/1.75 (r(s(z), s(s(s(s(s(z))))))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[60, 32])).
% 1.54/1.75 tff(62,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 1.54/1.75 tff(63,plain,
% 1.54/1.75 (s(s(s(z))) = s(s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[62])).
% 1.54/1.75 tff(64,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(65,plain,
% 1.54/1.75 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[64, 42])).
% 1.54/1.75 tff(66,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.54/1.75 tff(67,plain,
% 1.54/1.75 (s(s(z)) = s(s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[66])).
% 1.54/1.75 tff(68,plain,
% 1.54/1.75 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[67])).
% 1.54/1.75 tff(69,plain,
% 1.54/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(70,plain,
% 1.54/1.75 (inj_0(s(s(z))) = s(z)),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[69, 42])).
% 1.54/1.75 tff(71,plain,
% 1.54/1.75 (s(z) = inj_0(s(s(z)))),
% 1.54/1.75 inference(symmetry,[status(thm)],[70])).
% 1.54/1.75 tff(72,plain,
% 1.54/1.75 (s(z) = s(s(z))),
% 1.54/1.75 inference(transitivity,[status(thm)],[71, 68, 65])).
% 1.54/1.75 tff(73,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.54/1.75 tff(74,plain,
% 1.54/1.75 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[73])).
% 1.54/1.75 tff(75,plain,
% 1.54/1.75 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[74])).
% 1.54/1.75 tff(76,plain,
% 1.54/1.75 (s(z) = z),
% 1.54/1.75 inference(transitivity,[status(thm)],[71, 75, 44])).
% 1.54/1.75 tff(77,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[15, 76])).
% 1.54/1.75 tff(78,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(79,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[78, 72])).
% 1.54/1.75 tff(80,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(81,plain,
% 1.54/1.75 ($false),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[80, 63])).
% 1.54/1.75 tff(82,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.75 tff(83,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.75 tff(84,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.54/1.75 tff(85,plain,
% 1.54/1.75 ((z = s(z)) <=> (s(z) = z)),
% 1.54/1.75 inference(commutativity,[status(thm)],[])).
% 1.54/1.75 tff(86,plain,
% 1.54/1.75 ((s(z) = z) <=> (z = s(z))),
% 1.54/1.75 inference(symmetry,[status(thm)],[85])).
% 1.54/1.75 tff(87,plain,
% 1.54/1.75 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.54/1.75 inference(monotonicity,[status(thm)],[86])).
% 1.54/1.75 tff(88,plain,
% 1.54/1.75 (~(z = s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[15, 87])).
% 1.54/1.75 tff(89,plain,
% 1.54/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(90,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.54/1.75 inference(quant_inst,[status(thm)],[])).
% 1.54/1.75 tff(91,plain,
% 1.54/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.54/1.75 inference(modus_ponens,[status(thm)],[90, 89])).
% 1.54/1.75 tff(92,plain,
% 1.54/1.75 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[91, 25])).
% 1.54/1.75 tff(93,plain,
% 1.54/1.75 (b(z, s(z)) | r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[92, 88])).
% 1.54/1.75 tff(94,plain,
% 1.54/1.75 (r(z, s(z))),
% 1.54/1.75 inference(unit_resolution,[status(thm)],[93, 84])).
% 1.54/1.75 tff(95,assumption,(r(s(z), z)), introduced(assumption)).
% 1.54/1.75 tff(96,assumption,(r(z, s(z))), introduced(assumption)).
% 1.54/1.75 tff(97,plain,
% 1.54/1.75 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.54/1.75 inference(bind,[status(th)],[])).
% 1.54/1.75 tff(98,plain,
% 1.54/1.75 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.75 inference(quant_intro,[status(thm)],[97])).
% 1.54/1.75 tff(99,plain,
% 1.54/1.75 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.75 inference(rewrite,[status(thm)],[])).
% 1.54/1.75 tff(100,plain,
% 1.54/1.75 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(101,plain,
% 1.54/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[100])).
% 1.54/1.76 tff(102,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 1.54/1.76 tff(103,plain,
% 1.54/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.54/1.76 tff(104,plain,
% 1.54/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.54/1.76 tff(105,plain,(
% 1.54/1.76 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[104])).
% 1.54/1.76 tff(106,plain,
% 1.54/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.54/1.76 tff(107,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(108,plain,
% 1.54/1.76 (((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(109,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[108])).
% 1.54/1.76 tff(110,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[109, 107])).
% 1.54/1.76 tff(111,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(112,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.54/1.76 tff(113,plain,
% 1.54/1.76 (~r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[112, 106, 96, 2, 95])).
% 1.54/1.76 tff(114,plain,
% 1.54/1.76 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.54/1.76 inference(commutativity,[status(thm)],[])).
% 1.54/1.76 tff(115,plain,
% 1.54/1.76 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.54/1.76 inference(symmetry,[status(thm)],[114])).
% 1.54/1.76 tff(116,plain,
% 1.54/1.76 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[115])).
% 1.54/1.76 tff(117,plain,
% 1.54/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(118,plain,
% 1.54/1.76 (~(s(s(z)) = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[117, 13])).
% 1.54/1.76 tff(119,plain,
% 1.54/1.76 (~(z = s(s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[118, 116])).
% 1.54/1.76 tff(120,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(121,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(122,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.54/1.76 tff(123,plain,
% 1.54/1.76 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[122, 25])).
% 1.54/1.76 tff(124,plain,
% 1.54/1.76 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[123, 119])).
% 1.54/1.76 tff(125,plain,
% 1.54/1.76 (b(z, s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[124, 113])).
% 1.54/1.76 tff(126,assumption,(r(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(127,assumption,(r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.54/1.76 tff(128,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(129,plain,
% 1.54/1.76 (((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(130,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[129])).
% 1.54/1.76 tff(131,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[130, 128])).
% 1.54/1.76 tff(132,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(133,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[132, 131])).
% 1.54/1.76 tff(134,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[133, 106, 96, 95, 126, 127])).
% 1.54/1.76 tff(135,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(136,plain,
% 1.54/1.76 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[135, 96, 95, 126])).
% 1.54/1.76 tff(137,assumption,(~r(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.54/1.76 tff(138,assumption,(~b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.54/1.76 tff(139,plain,
% 1.54/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(140,plain,
% 1.54/1.76 (~(s(s(s(s(s(z))))) = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[139, 13])).
% 1.54/1.76 tff(141,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(142,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(143,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.54/1.76 tff(144,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[143, 25, 140, 138, 137])).
% 1.54/1.76 tff(145,plain,(b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(146,plain,
% 1.54/1.76 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[145, 136])).
% 1.54/1.76 tff(147,plain,
% 1.54/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(148,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(149,plain,
% 1.54/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.54/1.76 tff(150,plain,
% 1.54/1.76 (~r(s(s(z)), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[149, 106, 96, 2, 95])).
% 1.54/1.76 tff(151,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 1.54/1.76 tff(152,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.54/1.76 tff(153,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(154,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(155,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.54/1.76 tff(156,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[155, 25, 118, 152, 151])).
% 1.54/1.76 tff(157,plain,(b(s(s(z)), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(158,plain,
% 1.54/1.76 (b(s(s(z)), z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[157, 150])).
% 1.54/1.76 tff(159,assumption,(b(s(s(s(s(s(z))))), z)), introduced(assumption)).
% 1.54/1.76 tff(160,assumption,(b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(161,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.54/1.76 tff(162,plain,
% 1.54/1.76 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(163,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[162])).
% 1.54/1.76 tff(164,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(165,plain,
% 1.54/1.76 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) <=> ((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> (((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.54/1.76 inference(bind,[status(th)],[])).
% 1.54/1.76 tff(166,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(quant_intro,[status(thm)],[165])).
% 1.54/1.76 tff(167,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X1, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 1.54/1.76 tff(168,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.54/1.76 tff(169,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[168, 164])).
% 1.54/1.76 tff(170,plain,(
% 1.54/1.76 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(skolemize,[status(sab)],[169])).
% 1.54/1.76 tff(171,plain,
% 1.54/1.76 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[170, 163])).
% 1.54/1.76 tff(172,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(173,plain,
% 1.54/1.76 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), 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(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(174,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[173])).
% 1.54/1.76 tff(175,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[174, 172])).
% 1.54/1.76 tff(176,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(177,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[176, 175])).
% 1.54/1.76 tff(178,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[177, 171, 161, 1, 160, 159])).
% 1.54/1.76 tff(179,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(180,plain,
% 1.54/1.76 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[179, 158, 146, 125])).
% 1.54/1.76 tff(181,assumption,(s(s(z)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.76 tff(182,plain,
% 1.54/1.76 (s(s(s(s(s(z))))) = s(s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[181])).
% 1.54/1.76 tff(183,assumption,(s(s(s(s(s(z))))) = s(s(z))), introduced(assumption)).
% 1.54/1.76 tff(184,plain,
% 1.54/1.76 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[183])).
% 1.54/1.76 tff(185,plain,
% 1.54/1.76 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[184])).
% 1.54/1.76 tff(186,plain,
% 1.54/1.76 (s(z) = s(s(s(s(z))))),
% 1.54/1.76 inference(transitivity,[status(thm)],[71, 185, 48])).
% 1.54/1.76 tff(187,plain,
% 1.54/1.76 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[186])).
% 1.54/1.76 tff(188,plain,
% 1.54/1.76 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.54/1.76 inference(symmetry,[status(thm)],[187])).
% 1.54/1.76 tff(189,plain,
% 1.54/1.76 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(190,plain,
% 1.54/1.76 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[189, 42])).
% 1.54/1.76 tff(191,plain,
% 1.54/1.76 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.76 inference(symmetry,[status(thm)],[190])).
% 1.54/1.76 tff(192,plain,
% 1.54/1.76 (s(s(s(z))) = z),
% 1.54/1.76 inference(transitivity,[status(thm)],[191, 188, 44])).
% 1.54/1.76 tff(193,plain,
% 1.54/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(194,plain,
% 1.54/1.76 (~(s(s(s(z))) = z)),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[193, 13])).
% 1.54/1.76 tff(195,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[194, 192])).
% 1.54/1.76 tff(196,plain,(~(s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(197,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[196, 182])).
% 1.54/1.76 tff(198,plain,(~(s(s(z)) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(199,assumption,(~r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(200,assumption,(~b(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.76 tff(201,plain,
% 1.54/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(202,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(203,plain,
% 1.54/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.54/1.76 tff(204,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[203, 25, 200, 199, 198])).
% 1.54/1.76 tff(205,plain,(b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.76 tff(206,plain,
% 1.54/1.76 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[205, 180])).
% 1.54/1.76 tff(207,assumption,(b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.54/1.76 tff(208,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(209,plain,
% 1.54/1.76 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(rewrite,[status(thm)],[])).
% 1.54/1.76 tff(210,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.54/1.76 inference(monotonicity,[status(thm)],[209])).
% 1.54/1.76 tff(211,plain,
% 1.54/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.76 inference(transitivity,[status(thm)],[210, 208])).
% 1.54/1.76 tff(212,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.76 inference(quant_inst,[status(thm)],[])).
% 1.54/1.76 tff(213,plain,
% 1.54/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 1.54/1.76 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.54/1.76 tff(214,plain,
% 1.54/1.76 ($false),
% 1.54/1.76 inference(unit_resolution,[status(thm)],[213, 171, 161, 1, 207, 159])).
% 1.54/1.76 tff(215,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(216,plain,
% 1.54/1.77 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[215, 158, 146, 125])).
% 1.54/1.77 tff(217,assumption,(~(s(s(s(s(s(z))))) = s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(218,assumption,(~b(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(219,assumption,(~r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.54/1.77 tff(220,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(221,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(222,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(z))) | b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.54/1.77 tff(223,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[222, 25, 219, 218, 217])).
% 1.54/1.77 tff(224,plain,(b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))) | (s(s(s(s(s(z))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(225,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), s(s(z))) | r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[224, 196])).
% 1.54/1.77 tff(226,plain,
% 1.54/1.77 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[225, 216])).
% 1.54/1.77 tff(227,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(228,plain,
% 1.54/1.77 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(229,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[228])).
% 1.54/1.77 tff(230,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[229, 227])).
% 1.54/1.77 tff(231,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(232,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.54/1.77 tff(233,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[232, 106, 2, 126, 226, 206])).
% 1.54/1.77 tff(234,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(235,plain,
% 1.54/1.77 (~r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[234, 94, 61, 31])).
% 1.54/1.77 tff(236,plain,
% 1.54/1.77 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(237,plain,
% 1.54/1.77 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[236])).
% 1.54/1.77 tff(238,plain,
% 1.54/1.77 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[237])).
% 1.54/1.77 tff(239,plain,
% 1.54/1.77 (~(s(s(z)) = s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[78, 238])).
% 1.54/1.77 tff(240,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(241,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(242,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[241, 240])).
% 1.54/1.77 tff(243,plain,
% 1.54/1.77 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[242, 25])).
% 1.54/1.77 tff(244,plain,
% 1.54/1.77 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[243, 239])).
% 1.54/1.77 tff(245,plain,
% 1.54/1.77 (b(s(s(z)), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[244, 235])).
% 1.54/1.77 tff(246,plain,
% 1.54/1.77 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(247,plain,
% 1.54/1.77 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[246])).
% 1.54/1.77 tff(248,plain,
% 1.54/1.77 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[247])).
% 1.54/1.77 tff(249,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(250,plain,
% 1.54/1.77 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[249])).
% 1.54/1.77 tff(251,plain,
% 1.54/1.77 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.54/1.77 inference(symmetry,[status(thm)],[250])).
% 1.54/1.77 tff(252,plain,
% 1.54/1.77 (s(s(s(z))) = z),
% 1.54/1.77 inference(transitivity,[status(thm)],[191, 251, 44])).
% 1.54/1.77 tff(253,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[194, 252])).
% 1.54/1.77 tff(254,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(255,plain,
% 1.54/1.77 (~(s(s(s(s(z)))) = s(z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[254, 248])).
% 1.54/1.77 tff(256,plain,
% 1.54/1.77 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[135, 94, 31, 61])).
% 1.54/1.77 tff(257,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[145, 256])).
% 1.54/1.77 tff(258,assumption,(~b(z, elem!1)), introduced(assumption)).
% 1.54/1.77 tff(259,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.54/1.77 tff(260,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.77 tff(261,plain,
% 1.54/1.77 ((elem!1 = z) <=> (z = elem!1)),
% 1.54/1.77 inference(commutativity,[status(thm)],[])).
% 1.54/1.77 tff(262,plain,
% 1.54/1.77 ((z = elem!1) <=> (elem!1 = z)),
% 1.54/1.77 inference(symmetry,[status(thm)],[261])).
% 1.54/1.77 tff(263,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.77 tff(264,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(265,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(266,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[265, 264])).
% 1.54/1.77 tff(267,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[266, 106, 96, 95, 263])).
% 1.54/1.77 tff(268,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.54/1.77 tff(269,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.54/1.77 tff(270,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(271,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(272,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.54/1.77 tff(273,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[272, 25, 52, 269, 268])).
% 1.54/1.77 tff(274,plain,(b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(275,plain,
% 1.54/1.77 (b(s(s(s(s(z)))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[274, 267])).
% 1.54/1.77 tff(276,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(277,plain,
% 1.54/1.77 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(278,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[277])).
% 1.54/1.77 tff(279,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[278, 276])).
% 1.54/1.77 tff(280,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(281,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[280, 279])).
% 1.54/1.77 tff(282,plain,
% 1.54/1.77 (~r(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[281, 106, 96, 95, 263])).
% 1.54/1.77 tff(283,assumption,(z = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.77 tff(284,plain,
% 1.54/1.77 (s(s(s(s(z)))) = z),
% 1.54/1.77 inference(symmetry,[status(thm)],[283])).
% 1.54/1.77 tff(285,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[52, 284])).
% 1.54/1.77 tff(286,plain,(~(z = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(287,assumption,(~b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.77 tff(288,assumption,(~r(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.77 tff(289,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(290,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(291,plain,
% 1.54/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[290, 289])).
% 1.54/1.77 tff(292,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[291, 25, 288, 287, 286])).
% 1.54/1.77 tff(293,plain,(b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(294,plain,
% 1.54/1.77 (b(z, s(s(s(s(z)))))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[293, 282])).
% 1.54/1.77 tff(295,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(296,plain,
% 1.54/1.77 (((~r(s(s(s(s(s(z))))), z)) | (~r(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(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(297,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[296])).
% 1.54/1.77 tff(298,plain,
% 1.54/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[297, 295])).
% 1.54/1.77 tff(299,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(300,plain,
% 1.54/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[299, 298])).
% 1.54/1.77 tff(301,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[300, 106, 260, 126, 127, 263])).
% 1.54/1.77 tff(302,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(303,plain,
% 1.54/1.77 (~r(s(s(s(s(s(z))))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[302, 263, 126, 260])).
% 1.54/1.77 tff(304,plain,
% 1.54/1.77 (b(s(s(s(s(s(z))))), z)),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[145, 303])).
% 1.54/1.77 tff(305,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(306,plain,
% 1.54/1.77 (((~b(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(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))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(307,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.54/1.77 inference(monotonicity,[status(thm)],[306])).
% 1.54/1.77 tff(308,plain,
% 1.54/1.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.54/1.77 inference(transitivity,[status(thm)],[307, 305])).
% 1.54/1.77 tff(309,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.54/1.77 inference(quant_inst,[status(thm)],[])).
% 1.54/1.77 tff(310,plain,
% 1.54/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.54/1.77 inference(modus_ponens,[status(thm)],[309, 308])).
% 1.54/1.77 tff(311,plain,
% 1.54/1.77 ($false),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[310, 171, 83, 304, 294, 275])).
% 1.54/1.77 tff(312,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.77 tff(313,plain,
% 1.54/1.77 (~r(s(s(s(s(z)))), s(z))),
% 1.54/1.77 inference(unit_resolution,[status(thm)],[312, 260, 96, 95, 126, 83])).
% 1.54/1.77 tff(314,assumption,(~(s(s(s(s(z)))) = s(z))), introduced(assumption)).
% 1.54/1.77 tff(315,assumption,(~b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.77 tff(316,assumption,(~r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.77 tff(317,plain,
% 1.54/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.54/1.77 inference(rewrite,[status(thm)],[])).
% 1.54/1.77 tff(318,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(319,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.54/1.78 tff(320,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[319, 25, 316, 315, 314])).
% 1.54/1.78 tff(321,plain,(r(s(s(s(s(z)))), s(z)) | b(s(s(s(s(z)))), s(z)) | (s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(322,plain,
% 1.54/1.78 (b(s(s(s(s(z)))), s(z))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[321, 313, 255])).
% 1.54/1.78 tff(323,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(324,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(325,plain,
% 1.54/1.78 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(326,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[325])).
% 1.54/1.78 tff(327,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[326, 324])).
% 1.54/1.78 tff(328,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(329,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.54/1.78 tff(330,plain,
% 1.54/1.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[329, 171, 323, 259, 322])).
% 1.54/1.78 tff(331,assumption,(~b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(332,assumption,(~r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(333,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.78 tff(334,plain,
% 1.54/1.78 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[333])).
% 1.54/1.78 tff(335,plain,
% 1.54/1.78 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[334])).
% 1.54/1.78 tff(336,plain,
% 1.54/1.78 (s(s(s(z))) = s(z)),
% 1.54/1.78 inference(transitivity,[status(thm)],[191, 335, 70])).
% 1.54/1.78 tff(337,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 1.54/1.78 tff(338,plain,
% 1.54/1.78 (s(z) = s(s(s(z)))),
% 1.54/1.78 inference(symmetry,[status(thm)],[337])).
% 1.54/1.78 tff(339,plain,
% 1.54/1.78 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[338])).
% 1.54/1.78 tff(340,plain,
% 1.54/1.78 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.54/1.78 inference(symmetry,[status(thm)],[339])).
% 1.54/1.78 tff(341,plain,
% 1.54/1.78 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.54/1.78 inference(symmetry,[status(thm)],[65])).
% 1.54/1.78 tff(342,plain,
% 1.54/1.78 (s(s(z)) = z),
% 1.54/1.78 inference(transitivity,[status(thm)],[341, 340, 44])).
% 1.54/1.78 tff(343,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[118, 342])).
% 1.54/1.78 tff(344,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(345,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[344, 336])).
% 1.54/1.78 tff(346,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(347,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(348,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(349,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[348, 347])).
% 1.54/1.78 tff(350,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[349, 25, 346, 332, 331])).
% 1.54/1.78 tff(351,plain,(b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(352,plain,
% 1.54/1.78 (r(s(s(z)), s(s(s(s(z)))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[351, 330])).
% 1.54/1.78 tff(353,plain,
% 1.54/1.78 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.78 inference(commutativity,[status(thm)],[])).
% 1.54/1.78 tff(354,plain,
% 1.54/1.78 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[353])).
% 1.54/1.78 tff(355,plain,
% 1.54/1.78 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[346, 354])).
% 1.54/1.78 tff(356,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(357,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 1.54/1.78 tff(358,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(359,plain,
% 1.54/1.78 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(360,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[359])).
% 1.54/1.78 tff(361,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[360, 358])).
% 1.54/1.78 tff(362,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(363,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[362, 361])).
% 1.54/1.78 tff(364,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[363, 171, 323, 259, 357, 356])).
% 1.54/1.78 tff(365,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(366,plain,
% 1.54/1.78 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[365, 323, 259, 322])).
% 1.54/1.78 tff(367,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(368,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(369,assumption,(~(s(s(s(s(z)))) = s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(370,plain,
% 1.54/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(371,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(372,plain,
% 1.54/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[371, 370])).
% 1.54/1.78 tff(373,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[372, 25, 369, 368, 367])).
% 1.54/1.78 tff(374,plain,(b(s(s(s(s(z)))), s(s(z))) | (s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(375,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[374, 366, 355])).
% 1.54/1.78 tff(376,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.78 tff(377,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(378,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(379,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[378])).
% 1.54/1.78 tff(380,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[379, 377])).
% 1.54/1.78 tff(381,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(382,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[381, 380])).
% 1.54/1.78 tff(383,plain,
% 1.54/1.78 ($false),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[382, 171, 259, 4, 376, 207, 357])).
% 1.54/1.78 tff(384,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.78 tff(385,plain,
% 1.54/1.78 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[384, 259, 357, 4, 376])).
% 1.54/1.78 tff(386,plain,
% 1.54/1.78 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[225, 385])).
% 1.54/1.78 tff(387,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(388,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(389,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[388])).
% 1.54/1.78 tff(390,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.78 inference(transitivity,[status(thm)],[389, 387])).
% 1.54/1.78 tff(391,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.54/1.78 inference(quant_inst,[status(thm)],[])).
% 1.54/1.78 tff(392,plain,
% 1.54/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.78 inference(modus_ponens,[status(thm)],[391, 390])).
% 1.54/1.78 tff(393,plain,
% 1.54/1.78 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[392, 171, 259, 4, 376, 357])).
% 1.54/1.78 tff(394,plain,
% 1.54/1.78 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[203, 25, 393, 198])).
% 1.54/1.78 tff(395,plain,
% 1.54/1.78 (r(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.78 inference(unit_resolution,[status(thm)],[374, 367, 355])).
% 1.54/1.78 tff(396,assumption,(r(s(s(s(s(s(z))))), s(s(z)))), introduced(assumption)).
% 1.54/1.78 tff(397,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(398,plain,
% 1.54/1.78 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.78 inference(rewrite,[status(thm)],[])).
% 1.54/1.78 tff(399,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.54/1.78 inference(monotonicity,[status(thm)],[398])).
% 1.54/1.78 tff(400,plain,
% 1.54/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[399, 397])).
% 1.54/1.79 tff(401,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(402,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[401, 400])).
% 1.54/1.79 tff(403,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[402, 171, 4, 376, 357])).
% 1.54/1.79 tff(404,assumption,(s(s(s(s(z)))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(405,plain,
% 1.54/1.79 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[404])).
% 1.54/1.79 tff(406,plain,
% 1.54/1.79 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[191, 405, 48, 404])).
% 1.54/1.79 tff(407,assumption,(s(s(s(z))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(408,plain,
% 1.54/1.79 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[407])).
% 1.54/1.79 tff(409,plain,
% 1.54/1.79 (s(s(z)) = s(s(s(s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[341, 408, 48])).
% 1.54/1.79 tff(410,plain,
% 1.54/1.79 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[409])).
% 1.54/1.79 tff(411,plain,
% 1.54/1.79 (s(z) = s(s(s(s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[71, 410, 190, 407])).
% 1.54/1.79 tff(412,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[55, 411])).
% 1.54/1.79 tff(413,plain,(~(s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(414,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[413, 406])).
% 1.54/1.79 tff(415,plain,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(416,plain,
% 1.54/1.79 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.54/1.79 inference(commutativity,[status(thm)],[])).
% 1.54/1.79 tff(417,assumption,(s(s(s(s(s(z))))) = s(s(s(s(z))))), introduced(assumption)).
% 1.54/1.79 tff(418,plain,
% 1.54/1.79 (s(s(s(s(z)))) = s(s(s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.54/1.79 tff(419,assumption,(~(s(s(s(s(z)))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.79 tff(420,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[419, 418])).
% 1.54/1.79 tff(421,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(422,plain,
% 1.54/1.79 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[421, 415])).
% 1.54/1.79 tff(423,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(424,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(425,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.54/1.79 tff(426,plain,
% 1.54/1.79 ((s(s(s(s(s(z))))) = s(s(s(s(z))))) | b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[425, 25])).
% 1.54/1.79 tff(427,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) | r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[426, 422])).
% 1.54/1.79 tff(428,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[427, 403])).
% 1.54/1.79 tff(429,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(430,plain,
% 1.54/1.79 (((~r(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)))) | (~r(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(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(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(431,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[430])).
% 1.54/1.79 tff(432,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[431, 429])).
% 1.54/1.79 tff(433,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(434,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.54/1.79 tff(435,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[434, 106, 428, 396, 395, 394])).
% 1.54/1.79 tff(436,plain,(b(s(s(s(s(z)))), s(s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(437,plain,
% 1.54/1.79 (b(s(s(s(s(z)))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[436, 386, 4, 376, 357, 259])).
% 1.54/1.79 tff(438,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(439,plain,
% 1.54/1.79 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(440,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[439])).
% 1.54/1.79 tff(441,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[440, 438])).
% 1.54/1.79 tff(442,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(443,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[442, 441])).
% 1.54/1.79 tff(444,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[443, 171, 259, 376, 357, 437])).
% 1.54/1.79 tff(445,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(446,plain,
% 1.54/1.79 (~b(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[445, 4, 357, 259])).
% 1.54/1.79 tff(447,assumption,(~(s(z) = s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(448,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(449,assumption,(~r(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.79 tff(450,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(451,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(452,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[451, 450])).
% 1.54/1.79 tff(453,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[452, 25, 449, 448, 447])).
% 1.54/1.79 tff(454,plain,(r(s(z), s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | (s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(455,plain,
% 1.54/1.79 (r(s(z), s(s(s(s(z)))))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[454, 446, 254])).
% 1.54/1.79 tff(456,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(457,plain,
% 1.54/1.79 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(458,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[457])).
% 1.54/1.79 tff(459,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[458, 456])).
% 1.54/1.79 tff(460,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(461,plain,
% 1.54/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[460, 459])).
% 1.54/1.79 tff(462,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[461, 106, 260, 126, 3, 396])).
% 1.54/1.79 tff(463,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(464,plain,
% 1.54/1.79 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[463, 455, 126, 260])).
% 1.54/1.79 tff(465,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[225, 464])).
% 1.54/1.79 tff(466,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(467,plain,
% 1.54/1.79 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(468,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.79 inference(monotonicity,[status(thm)],[467])).
% 1.54/1.79 tff(469,plain,
% 1.54/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.79 inference(transitivity,[status(thm)],[468, 466])).
% 1.54/1.79 tff(470,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(471,plain,
% 1.54/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[470, 469])).
% 1.54/1.79 tff(472,plain,
% 1.54/1.79 ($false),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[471, 171, 323, 259, 4, 465])).
% 1.54/1.79 tff(473,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.79 tff(474,plain,
% 1.54/1.79 (~b(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[473, 323, 259, 126, 260, 322])).
% 1.54/1.79 tff(475,plain,
% 1.54/1.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(476,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.79 inference(quant_inst,[status(thm)],[])).
% 1.54/1.79 tff(477,plain,
% 1.54/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(modus_ponens,[status(thm)],[476, 475])).
% 1.54/1.79 tff(478,plain,
% 1.54/1.79 ((s(s(s(s(s(z))))) = s(z)) | b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[477, 25])).
% 1.54/1.79 tff(479,plain,
% 1.54/1.79 (b(s(s(s(s(s(z))))), s(z)) | r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[478, 54])).
% 1.54/1.79 tff(480,plain,
% 1.54/1.79 (r(s(s(s(s(s(z))))), s(z))),
% 1.54/1.79 inference(unit_resolution,[status(thm)],[479, 474])).
% 1.54/1.79 tff(481,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(482,plain,
% 1.54/1.79 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.79 inference(rewrite,[status(thm)],[])).
% 1.54/1.79 tff(483,plain,
% 1.54/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.54/1.80 inference(monotonicity,[status(thm)],[482])).
% 1.54/1.80 tff(484,plain,
% 1.54/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.54/1.80 inference(transitivity,[status(thm)],[483, 481])).
% 1.54/1.80 tff(485,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.54/1.80 inference(quant_inst,[status(thm)],[])).
% 1.54/1.80 tff(486,plain,
% 1.54/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.54/1.80 inference(modus_ponens,[status(thm)],[485, 484])).
% 1.54/1.80 tff(487,plain,
% 1.54/1.80 (~r(z, s(s(s(s(s(z))))))),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[486, 106, 96, 95, 480])).
% 1.54/1.80 tff(488,assumption,(z = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.54/1.80 tff(489,plain,
% 1.54/1.80 (s(s(s(s(s(z))))) = z),
% 1.54/1.80 inference(symmetry,[status(thm)],[488])).
% 1.54/1.80 tff(490,plain,
% 1.54/1.80 ($false),
% 1.54/1.80 inference(unit_resolution,[status(thm)],[140, 489])).
% 1.54/1.80 tff(491,plain,(~(z = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.54/1.80 tff(492,assumption,(~b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.80 tff(493,assumption,(~r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.54/1.80 tff(494,plain,
% 1.54/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.54/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(495,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(496,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[495, 494])).
% 1.64/1.80 tff(497,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[496, 25, 493, 492, 491])).
% 1.64/1.80 tff(498,plain,(b(z, s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(499,plain,
% 1.64/1.80 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[498, 487])).
% 1.64/1.80 tff(500,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.80 tff(501,assumption,(r(s(s(z)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.80 tff(502,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 1.64/1.80 tff(503,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(504,plain,
% 1.64/1.80 (((~r(s(s(s(s(s(z))))), 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(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(505,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[504])).
% 1.64/1.80 tff(506,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[505, 503])).
% 1.64/1.80 tff(507,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(508,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[507, 506])).
% 1.64/1.80 tff(509,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[508, 106, 260, 502, 501, 500])).
% 1.64/1.80 tff(510,plain,((~r(s(s(s(s(s(z))))), 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(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(511,plain,
% 1.64/1.80 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[510, 352, 260, 480])).
% 1.64/1.80 tff(512,plain,
% 1.64/1.80 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[205, 511])).
% 1.64/1.80 tff(513,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(514,plain,
% 1.64/1.80 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), 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(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(515,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[514])).
% 1.64/1.80 tff(516,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(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(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[515, 513])).
% 1.64/1.80 tff(517,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(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(z, s(s(z)))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(518,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[517, 516])).
% 1.64/1.80 tff(519,plain,
% 1.64/1.80 (~b(z, s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[518, 171, 259, 83, 512, 322, 499])).
% 1.64/1.80 tff(520,plain,
% 1.64/1.80 (r(z, s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[124, 519])).
% 1.64/1.80 tff(521,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(522,plain,
% 1.64/1.80 (((~r(s(s(z)), s(s(s(s(z)))))) | (~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(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(523,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[522])).
% 1.64/1.80 tff(524,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[523, 521])).
% 1.64/1.80 tff(525,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(526,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[525, 524])).
% 1.64/1.80 tff(527,plain,
% 1.64/1.80 (~r(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[526, 106, 520, 375, 352])).
% 1.64/1.80 tff(528,plain,
% 1.64/1.80 (b(z, s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[293, 527])).
% 1.64/1.80 tff(529,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(530,plain,
% 1.64/1.80 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(531,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[530])).
% 1.64/1.80 tff(532,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[531, 529])).
% 1.64/1.80 tff(533,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(534,plain,
% 1.64/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[533, 532])).
% 1.64/1.80 tff(535,plain,
% 1.64/1.80 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[534, 106, 260, 126, 480])).
% 1.64/1.80 tff(536,plain,
% 1.64/1.80 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[454, 535, 254])).
% 1.64/1.80 tff(537,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(538,plain,
% 1.64/1.80 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(539,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.64/1.80 inference(monotonicity,[status(thm)],[538])).
% 1.64/1.80 tff(540,plain,
% 1.64/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.64/1.80 inference(transitivity,[status(thm)],[539, 537])).
% 1.64/1.80 tff(541,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(542,plain,
% 1.64/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[541, 540])).
% 1.64/1.80 tff(543,plain,
% 1.64/1.80 ($false),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[542, 171, 83, 536, 322, 499, 528])).
% 1.64/1.80 tff(544,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.80 tff(545,plain,
% 1.64/1.80 (~b(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[544, 260, 259, 83, 126, 94, 95])).
% 1.64/1.80 tff(546,plain,
% 1.64/1.80 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.64/1.80 inference(rewrite,[status(thm)],[])).
% 1.64/1.80 tff(547,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.64/1.80 inference(quant_inst,[status(thm)],[])).
% 1.64/1.80 tff(548,plain,
% 1.64/1.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.80 inference(modus_ponens,[status(thm)],[547, 546])).
% 1.64/1.80 tff(549,plain,
% 1.64/1.80 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[548, 25])).
% 1.64/1.80 tff(550,plain,
% 1.64/1.80 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[549, 78])).
% 1.64/1.80 tff(551,plain,
% 1.64/1.80 (r(s(z), s(s(z)))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[550, 545])).
% 1.64/1.80 tff(552,plain,
% 1.64/1.80 (~r(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[312, 260, 94, 95, 126, 83])).
% 1.64/1.80 tff(553,plain,
% 1.64/1.80 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[321, 552, 255])).
% 1.64/1.80 tff(554,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.64/1.80 tff(555,plain,
% 1.64/1.80 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[445, 376, 357, 259])).
% 1.64/1.80 tff(556,plain,
% 1.64/1.80 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.80 inference(unit_resolution,[status(thm)],[479, 555])).
% 1.64/1.80 tff(557,plain,
% 1.64/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(558,plain,
% 1.64/1.81 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(559,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[558])).
% 1.64/1.81 tff(560,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[559, 557])).
% 1.64/1.81 tff(561,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(562,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[561, 560])).
% 1.64/1.81 tff(563,plain,
% 1.64/1.81 (~r(z, s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[562, 106, 554, 96, 556])).
% 1.64/1.81 tff(564,plain,
% 1.64/1.81 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[498, 563])).
% 1.64/1.81 tff(565,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[443, 171, 259, 376, 357, 356])).
% 1.64/1.81 tff(566,plain,((~b(s(s(s(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(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(567,plain,
% 1.64/1.81 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[566, 376, 259, 357])).
% 1.64/1.81 tff(568,plain,
% 1.64/1.81 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[374, 567, 355])).
% 1.64/1.81 tff(569,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.64/1.81 tff(570,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(571,plain,
% 1.64/1.81 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(572,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[571])).
% 1.64/1.81 tff(573,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[572, 570])).
% 1.64/1.81 tff(574,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(575,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[574, 573])).
% 1.64/1.81 tff(576,plain,
% 1.64/1.81 (~r(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[575, 106, 554, 569, 501])).
% 1.64/1.81 tff(577,plain,
% 1.64/1.81 (b(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[454, 576, 254])).
% 1.64/1.81 tff(578,plain,
% 1.64/1.81 (~b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[445, 577, 357, 259])).
% 1.64/1.81 tff(579,plain,
% 1.64/1.81 (r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[479, 578])).
% 1.64/1.81 tff(580,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(581,plain,
% 1.64/1.81 (((~r(s(s(s(s(s(z))))), s(z))) | (~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(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(s(z))))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(582,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[581])).
% 1.64/1.81 tff(583,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[582, 580])).
% 1.64/1.81 tff(584,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~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)))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(585,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.64/1.81 tff(586,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[585, 106, 260, 579, 569, 501])).
% 1.64/1.81 tff(587,plain,((~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)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(588,plain,
% 1.64/1.81 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[587, 568, 554, 260, 259, 357])).
% 1.64/1.81 tff(589,plain,
% 1.64/1.81 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[205, 588])).
% 1.64/1.81 tff(590,plain,
% 1.64/1.81 (~b(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[518, 171, 259, 83, 589, 357, 564])).
% 1.64/1.81 tff(591,plain,
% 1.64/1.81 (r(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[124, 590])).
% 1.64/1.81 tff(592,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(593,plain,
% 1.64/1.81 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(594,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[593])).
% 1.64/1.81 tff(595,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[594, 592])).
% 1.64/1.81 tff(596,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(597,plain,
% 1.64/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[596, 595])).
% 1.64/1.81 tff(598,plain,
% 1.64/1.81 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[597, 171, 259, 376, 357])).
% 1.64/1.81 tff(599,plain,
% 1.64/1.81 (r(s(s(z)), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[351, 598])).
% 1.64/1.81 tff(600,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.64/1.81 tff(601,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(602,plain,
% 1.64/1.81 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(603,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[602])).
% 1.64/1.81 tff(604,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[603, 601])).
% 1.64/1.81 tff(605,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(606,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.64/1.81 tff(607,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[606, 106, 554, 95, 600, 500])).
% 1.64/1.81 tff(608,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(609,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[608, 599, 591, 95, 554])).
% 1.64/1.81 tff(610,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(611,plain,
% 1.64/1.81 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[610, 551, 95, 259, 553, 83, 94, 260])).
% 1.64/1.81 tff(612,plain,
% 1.64/1.81 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[454, 611, 254])).
% 1.64/1.81 tff(613,plain,
% 1.64/1.81 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[463, 612, 126, 260])).
% 1.64/1.81 tff(614,plain,
% 1.64/1.81 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[225, 613])).
% 1.64/1.81 tff(615,plain,
% 1.64/1.81 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[587, 501, 551, 260, 259, 553])).
% 1.64/1.81 tff(616,plain,
% 1.64/1.81 (b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[374, 615, 355])).
% 1.64/1.81 tff(617,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(618,plain,
% 1.64/1.81 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(619,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[618])).
% 1.64/1.81 tff(620,plain,
% 1.64/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[619, 617])).
% 1.64/1.81 tff(621,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.64/1.81 inference(quant_inst,[status(thm)],[])).
% 1.64/1.81 tff(622,plain,
% 1.64/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.64/1.81 inference(modus_ponens,[status(thm)],[621, 620])).
% 1.64/1.81 tff(623,plain,
% 1.64/1.81 ($false),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[622, 106, 554, 96, 600, 501])).
% 1.64/1.81 tff(624,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.81 tff(625,plain,
% 1.64/1.81 (~r(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[624, 501, 94, 551])).
% 1.64/1.81 tff(626,plain,
% 1.64/1.81 (b(z, s(s(z)))),
% 1.64/1.81 inference(unit_resolution,[status(thm)],[124, 625])).
% 1.64/1.81 tff(627,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(628,plain,
% 1.64/1.81 (((~b(z, 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(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(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(rewrite,[status(thm)],[])).
% 1.64/1.81 tff(629,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.81 inference(monotonicity,[status(thm)],[628])).
% 1.64/1.81 tff(630,plain,
% 1.64/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.81 inference(transitivity,[status(thm)],[629, 627])).
% 1.64/1.82 tff(631,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(632,plain,
% 1.64/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.64/1.82 tff(633,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[632, 171, 161, 1, 83, 207, 356])).
% 1.64/1.82 tff(634,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, 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))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(635,plain,
% 1.64/1.82 (~b(s(s(z)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[634, 626, 83, 616, 614])).
% 1.64/1.82 tff(636,plain,
% 1.64/1.82 (r(s(s(z)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[157, 635])).
% 1.64/1.82 tff(637,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.64/1.82 tff(638,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.64/1.82 tff(639,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(640,plain,
% 1.64/1.82 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(641,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[640])).
% 1.64/1.82 tff(642,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.64/1.82 inference(transitivity,[status(thm)],[641, 639])).
% 1.64/1.82 tff(643,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(644,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, elem!1))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[643, 642])).
% 1.64/1.82 tff(645,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[644, 106, 638, 554, 637, 95])).
% 1.64/1.82 tff(646,plain,((~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(647,plain,
% 1.64/1.82 (~r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[646, 636, 551, 95])).
% 1.64/1.82 tff(648,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(649,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(650,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[649, 648])).
% 1.64/1.82 tff(651,plain,
% 1.64/1.82 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[650, 25])).
% 1.64/1.82 tff(652,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[651, 647, 258])).
% 1.64/1.82 tff(653,plain,
% 1.64/1.82 (elem!1 = z),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[652, 262])).
% 1.64/1.82 tff(654,plain,
% 1.64/1.82 (~b(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[365, 357, 259, 356])).
% 1.64/1.82 tff(655,plain,
% 1.64/1.82 (r(s(z), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[550, 654])).
% 1.64/1.82 tff(656,plain,
% 1.64/1.82 (~b(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[566, 357, 259, 356])).
% 1.64/1.82 tff(657,plain,
% 1.64/1.82 (r(s(z), s(s(s(s(z)))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[454, 656, 254])).
% 1.64/1.82 tff(658,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[463, 657, 126, 260])).
% 1.64/1.82 tff(659,plain,
% 1.64/1.82 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[225, 658])).
% 1.64/1.82 tff(660,plain,
% 1.64/1.82 (~b(s(s(z)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[634, 659, 83, 356, 161])).
% 1.64/1.82 tff(661,plain,
% 1.64/1.82 (r(s(s(z)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[157, 660])).
% 1.64/1.82 tff(662,plain,
% 1.64/1.82 (~r(z, elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[646, 661, 655, 95])).
% 1.64/1.82 tff(663,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[651, 662, 258])).
% 1.64/1.82 tff(664,plain,
% 1.64/1.82 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[663])).
% 1.64/1.82 tff(665,plain,
% 1.64/1.82 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.64/1.82 inference(symmetry,[status(thm)],[664])).
% 1.64/1.82 tff(666,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 1.64/1.82 tff(667,plain,
% 1.64/1.82 (b(s(s(z)), z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[666, 665])).
% 1.64/1.82 tff(668,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[660, 667])).
% 1.64/1.82 tff(669,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)) | b(z, elem!1) | (~r(s(z), z)) | (~b(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)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(670,plain,
% 1.64/1.82 (~b(s(s(z)), elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[669, 626, 258, 95, 83, 616, 553, 126, 260, 259])).
% 1.64/1.82 tff(671,plain,
% 1.64/1.82 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 1.64/1.82 inference(commutativity,[status(thm)],[])).
% 1.64/1.82 tff(672,assumption,(z = elem!1), introduced(assumption)).
% 1.64/1.82 tff(673,plain,
% 1.64/1.82 ((s(z) = z) <=> (s(z) = elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[672])).
% 1.64/1.82 tff(674,plain,
% 1.64/1.82 ((s(z) = z) <=> (elem!1 = s(z))),
% 1.64/1.82 inference(transitivity,[status(thm)],[673, 671])).
% 1.64/1.82 tff(675,plain,
% 1.64/1.82 ((elem!1 = s(z)) <=> (s(z) = z)),
% 1.64/1.82 inference(symmetry,[status(thm)],[674])).
% 1.64/1.82 tff(676,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.64/1.82 tff(677,plain,
% 1.64/1.82 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[672])).
% 1.64/1.82 tff(678,plain,
% 1.64/1.82 (b(elem!1, s(z)) <=> b(z, s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[677])).
% 1.64/1.82 tff(679,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.64/1.82 tff(680,plain,
% 1.64/1.82 (b(z, s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[679, 678])).
% 1.64/1.82 tff(681,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[84, 680])).
% 1.64/1.82 tff(682,plain,((~(z = elem!1)) | b(z, s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(683,plain,
% 1.64/1.82 (~b(elem!1, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[682, 672, 84])).
% 1.64/1.82 tff(684,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(685,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(686,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[685, 684])).
% 1.64/1.82 tff(687,plain,
% 1.64/1.82 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[686, 25])).
% 1.64/1.82 tff(688,plain,
% 1.64/1.82 (elem!1 = s(z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[687, 683, 676])).
% 1.64/1.82 tff(689,plain,
% 1.64/1.82 (s(z) = z),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[688, 675])).
% 1.64/1.82 tff(690,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[15, 689])).
% 1.64/1.82 tff(691,plain,((~(z = elem!1)) | r(elem!1, s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(692,plain,
% 1.64/1.82 (r(elem!1, s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[691, 652, 84])).
% 1.64/1.82 tff(693,assumption,(elem!1 = z), introduced(assumption)).
% 1.64/1.82 tff(694,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[693, 261])).
% 1.64/1.82 tff(695,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.64/1.82 tff(696,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[695, 694])).
% 1.64/1.82 tff(697,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(698,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[697, 693])).
% 1.64/1.82 tff(699,plain,
% 1.64/1.82 (s(z) = s(elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[672])).
% 1.64/1.82 tff(700,plain,
% 1.64/1.82 (s(elem!1) = s(z)),
% 1.64/1.82 inference(symmetry,[status(thm)],[699])).
% 1.64/1.82 tff(701,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.64/1.82 tff(702,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[701, 700])).
% 1.64/1.82 tff(703,plain,((~(z = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(704,plain,
% 1.64/1.82 (s(elem!1) = s(z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[703, 698])).
% 1.64/1.82 tff(705,plain,
% 1.64/1.82 (s(s(elem!1)) = s(s(z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[704])).
% 1.64/1.82 tff(706,plain,
% 1.64/1.82 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[705])).
% 1.64/1.82 tff(707,plain,
% 1.64/1.82 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[706])).
% 1.64/1.82 tff(708,plain,
% 1.64/1.82 ((~b(s(s(z)), s(s(s(s(s(z))))))) <=> (~b(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[707])).
% 1.64/1.82 tff(709,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.64/1.82 tff(710,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.64/1.82 tff(711,plain,
% 1.64/1.82 (s(s(elem!1)) = s(s(z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[710])).
% 1.64/1.82 tff(712,plain,
% 1.64/1.82 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[711])).
% 1.64/1.82 tff(713,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[712])).
% 1.64/1.82 tff(714,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = s(z)),
% 1.64/1.82 inference(transitivity,[status(thm)],[713, 709])).
% 1.64/1.82 tff(715,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.64/1.82 tff(716,plain,
% 1.64/1.82 (s(z) = s(s(s(s(elem!1))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[715])).
% 1.64/1.82 tff(717,plain,
% 1.64/1.82 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[716])).
% 1.64/1.82 tff(718,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.64/1.82 inference(symmetry,[status(thm)],[717])).
% 1.64/1.82 tff(719,plain,
% 1.64/1.82 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(720,plain,
% 1.64/1.82 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[719, 42])).
% 1.64/1.82 tff(721,plain,
% 1.64/1.82 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[720])).
% 1.64/1.82 tff(722,plain,
% 1.64/1.82 (s(s(s(elem!1))) = z),
% 1.64/1.82 inference(transitivity,[status(thm)],[721, 718, 44])).
% 1.64/1.82 tff(723,plain,
% 1.64/1.82 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(724,plain,
% 1.64/1.82 (~(s(s(s(elem!1))) = z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[723, 13])).
% 1.64/1.82 tff(725,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[724, 722])).
% 1.64/1.82 tff(726,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(727,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[726, 714])).
% 1.64/1.82 tff(728,plain,((~(s(s(s(s(z)))) = s(z))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(729,plain,
% 1.64/1.82 (~(s(s(s(s(z)))) = s(z))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[728, 704])).
% 1.64/1.82 tff(730,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.64/1.82 tff(731,plain,
% 1.64/1.82 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[693])).
% 1.64/1.82 tff(732,plain,
% 1.64/1.82 ((~b(s(s(z)), elem!1)) <=> (~b(s(s(z)), z))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[731])).
% 1.64/1.82 tff(733,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 1.64/1.82 tff(734,plain,
% 1.64/1.82 (~b(s(s(z)), z)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[733, 732])).
% 1.64/1.82 tff(735,plain,
% 1.64/1.82 (r(s(s(z)), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[155, 25, 118, 734])).
% 1.64/1.82 tff(736,plain,
% 1.64/1.82 (s(s(z)) = s(s(elem!1))),
% 1.64/1.82 inference(symmetry,[status(thm)],[705])).
% 1.64/1.82 tff(737,plain,
% 1.64/1.82 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[736])).
% 1.64/1.82 tff(738,plain,
% 1.64/1.82 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.82 inference(symmetry,[status(thm)],[737])).
% 1.64/1.82 tff(739,assumption,(s(s(elem!1)) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.64/1.82 tff(740,plain,
% 1.64/1.82 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.64/1.82 inference(symmetry,[status(thm)],[739])).
% 1.64/1.82 tff(741,plain,
% 1.64/1.82 (s(s(s(s(s(z))))) = s(s(z))),
% 1.64/1.82 inference(transitivity,[status(thm)],[740, 711])).
% 1.64/1.82 tff(742,plain,
% 1.64/1.82 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[741])).
% 1.64/1.82 tff(743,plain,
% 1.64/1.82 (s(s(s(s(elem!1)))) = s(z)),
% 1.64/1.82 inference(transitivity,[status(thm)],[713, 49, 742, 70])).
% 1.64/1.82 tff(744,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[726, 743])).
% 1.64/1.82 tff(745,plain,((~(s(s(elem!1)) = s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(746,plain,
% 1.64/1.82 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[745, 704])).
% 1.64/1.82 tff(747,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.64/1.82 tff(748,plain,
% 1.64/1.82 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[693])).
% 1.64/1.82 tff(749,plain,
% 1.64/1.82 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(symmetry,[status(thm)],[748])).
% 1.64/1.82 tff(750,plain,
% 1.64/1.82 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[749])).
% 1.64/1.82 tff(751,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(752,plain,
% 1.64/1.82 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(753,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[752])).
% 1.64/1.82 tff(754,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[753, 751])).
% 1.64/1.82 tff(755,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(756,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[755, 754])).
% 1.64/1.82 tff(757,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[756, 106, 96, 95, 502])).
% 1.64/1.82 tff(758,plain,
% 1.64/1.82 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[757, 750])).
% 1.64/1.82 tff(759,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = elem!1) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.82 inference(commutativity,[status(thm)],[])).
% 1.64/1.82 tff(760,plain,
% 1.64/1.82 ((elem!1 = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.82 inference(symmetry,[status(thm)],[759])).
% 1.64/1.82 tff(761,plain,
% 1.64/1.82 (z = elem!1),
% 1.64/1.82 inference(symmetry,[status(thm)],[693])).
% 1.64/1.82 tff(762,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.82 tff(763,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[762, 759])).
% 1.64/1.82 tff(764,plain,
% 1.64/1.82 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.82 inference(transitivity,[status(thm)],[763, 760])).
% 1.64/1.82 tff(765,plain,
% 1.64/1.82 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[764])).
% 1.64/1.82 tff(766,plain,
% 1.64/1.82 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[140, 765])).
% 1.64/1.82 tff(767,plain,
% 1.64/1.82 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[763])).
% 1.64/1.82 tff(768,plain,
% 1.64/1.82 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[140, 767])).
% 1.64/1.82 tff(769,assumption,(r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.82 tff(770,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(771,plain,
% 1.64/1.82 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(772,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[771])).
% 1.64/1.82 tff(773,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.82 inference(transitivity,[status(thm)],[772, 770])).
% 1.64/1.82 tff(774,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(775,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[774, 773])).
% 1.64/1.82 tff(776,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[775, 106, 730, 95, 769, 502])).
% 1.64/1.82 tff(777,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(778,plain,
% 1.64/1.82 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[777, 502, 95, 730])).
% 1.64/1.82 tff(779,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(780,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z)))))))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(781,plain,
% 1.64/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[780, 779])).
% 1.64/1.82 tff(782,plain,
% 1.64/1.82 ((elem!1 = s(s(s(s(s(z)))))) | b(elem!1, s(s(s(s(s(z)))))) | r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[781, 25])).
% 1.64/1.82 tff(783,plain,
% 1.64/1.82 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[782, 778, 768])).
% 1.64/1.82 tff(784,plain,
% 1.64/1.82 (elem!1 = z),
% 1.64/1.82 inference(symmetry,[status(thm)],[672])).
% 1.64/1.82 tff(785,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.64/1.82 tff(786,plain,
% 1.64/1.82 (s(s(s(z))) = z),
% 1.64/1.82 inference(transitivity,[status(thm)],[785, 784])).
% 1.64/1.82 tff(787,plain,
% 1.64/1.82 ($false),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[194, 786])).
% 1.64/1.82 tff(788,plain,((~(s(s(s(z))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.82 tff(789,plain,
% 1.64/1.82 (~(s(s(s(z))) = elem!1)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[788, 698])).
% 1.64/1.82 tff(790,plain,
% 1.64/1.82 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.82 tff(791,plain,
% 1.64/1.82 ((~r(s(s(s(z))), z)) <=> (~r(s(s(s(z))), elem!1))),
% 1.64/1.82 inference(monotonicity,[status(thm)],[790])).
% 1.64/1.82 tff(792,plain,
% 1.64/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.64/1.82 inference(rewrite,[status(thm)],[])).
% 1.64/1.82 tff(793,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.64/1.82 inference(quant_inst,[status(thm)],[])).
% 1.64/1.82 tff(794,plain,
% 1.64/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[793, 792])).
% 1.64/1.82 tff(795,plain,
% 1.64/1.82 (~r(s(s(s(z))), z)),
% 1.64/1.82 inference(unit_resolution,[status(thm)],[794, 106, 96, 95, 747])).
% 1.64/1.82 tff(796,plain,
% 1.64/1.82 (~r(s(s(s(z))), elem!1)),
% 1.64/1.82 inference(modus_ponens,[status(thm)],[795, 791])).
% 1.64/1.82 tff(797,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.64/1.82 tff(798,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.64/1.82 tff(799,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.64/1.82 tff(800,plain,
% 1.64/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(801,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(802,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[801, 800])).
% 1.64/1.83 tff(803,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[802, 25, 799, 798, 797])).
% 1.64/1.83 tff(804,plain,(b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(805,plain,
% 1.64/1.83 (b(s(s(s(z))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[804, 796, 789])).
% 1.64/1.83 tff(806,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.64/1.83 tff(807,plain,
% 1.64/1.83 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[806])).
% 1.64/1.83 tff(808,plain,
% 1.64/1.83 (s(s(s(elem!1))) = s(z)),
% 1.64/1.83 inference(transitivity,[status(thm)],[712, 191, 807, 70])).
% 1.64/1.83 tff(809,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.64/1.83 tff(810,plain,
% 1.64/1.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[809])).
% 1.64/1.83 tff(811,plain,
% 1.64/1.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(812,plain,
% 1.64/1.83 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[811, 42])).
% 1.64/1.83 tff(813,plain,
% 1.64/1.83 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[812])).
% 1.64/1.83 tff(814,plain,
% 1.64/1.83 (s(s(elem!1)) = z),
% 1.64/1.83 inference(transitivity,[status(thm)],[813, 810, 44])).
% 1.64/1.83 tff(815,plain,
% 1.64/1.83 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(816,plain,
% 1.64/1.83 (~(s(s(elem!1)) = z)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[815, 13])).
% 1.64/1.83 tff(817,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[816, 814])).
% 1.64/1.83 tff(818,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(819,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[818, 808])).
% 1.64/1.83 tff(820,plain,((~(s(s(s(s(z)))) = s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(821,plain,
% 1.64/1.83 (~(s(s(s(s(z)))) = s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[820, 704])).
% 1.64/1.83 tff(822,plain,
% 1.64/1.83 (s(s(s(s(s(z))))) = s(s(s(z)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[407])).
% 1.64/1.83 tff(823,plain,
% 1.64/1.83 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[822])).
% 1.64/1.83 tff(824,plain,
% 1.64/1.83 (s(s(s(s(z)))) = s(s(z))),
% 1.64/1.83 inference(transitivity,[status(thm)],[49, 823, 65])).
% 1.64/1.83 tff(825,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[369, 824])).
% 1.64/1.83 tff(826,plain,((~(s(s(s(z))) = s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(827,plain,
% 1.64/1.83 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[826, 821])).
% 1.64/1.83 tff(828,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(829,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(830,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[829, 828])).
% 1.64/1.83 tff(831,plain,
% 1.64/1.83 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[830, 106, 95, 502, 747])).
% 1.64/1.83 tff(832,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(833,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(834,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.64/1.83 tff(835,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(s(s(s(z)))))) | b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[834, 25])).
% 1.64/1.83 tff(836,plain,
% 1.64/1.83 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[835, 831, 827])).
% 1.64/1.83 tff(837,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.64/1.83 tff(838,assumption,(b(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.83 tff(839,assumption,(b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.64/1.83 tff(840,assumption,(b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.83 tff(841,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(842,plain,
% 1.64/1.83 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(843,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[842])).
% 1.64/1.83 tff(844,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[843, 841])).
% 1.64/1.83 tff(845,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(846,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[845, 844])).
% 1.64/1.83 tff(847,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[846, 171, 840, 839, 838, 837])).
% 1.64/1.83 tff(848,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(849,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[848, 836, 805, 783])).
% 1.64/1.83 tff(850,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(851,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(852,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.64/1.83 tff(853,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = elem!1) | b(s(s(s(s(s(z))))), elem!1) | r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[852, 25])).
% 1.64/1.83 tff(854,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[853, 849, 766])).
% 1.64/1.83 tff(855,plain,
% 1.64/1.83 ($false),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[854, 758])).
% 1.64/1.83 tff(856,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.83 tff(857,plain,
% 1.64/1.83 (~r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[856, 747, 95, 693, 96, 730])).
% 1.64/1.83 tff(858,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[479, 857])).
% 1.64/1.83 tff(859,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(860,plain,
% 1.64/1.83 (((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(861,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[860])).
% 1.64/1.83 tff(862,plain,
% 1.64/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.64/1.83 inference(transitivity,[status(thm)],[861, 859])).
% 1.64/1.83 tff(863,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(864,plain,
% 1.64/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[863, 862])).
% 1.64/1.83 tff(865,plain,
% 1.64/1.83 (~r(s(z), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[864, 106, 96, 637, 95])).
% 1.64/1.83 tff(866,plain,
% 1.64/1.83 (b(s(z), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[550, 865])).
% 1.64/1.83 tff(867,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(868,plain,
% 1.64/1.83 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(869,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[868])).
% 1.64/1.83 tff(870,plain,
% 1.64/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.83 inference(transitivity,[status(thm)],[869, 867])).
% 1.64/1.83 tff(871,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(872,plain,
% 1.64/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[871, 870])).
% 1.64/1.83 tff(873,plain,
% 1.64/1.83 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[872, 171, 866, 259, 858])).
% 1.64/1.83 tff(874,plain,
% 1.64/1.83 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[873, 708])).
% 1.64/1.83 tff(875,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(876,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(877,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[876, 875])).
% 1.64/1.83 tff(878,plain,
% 1.64/1.83 ((s(s(elem!1)) = s(s(s(s(s(z)))))) | b(s(s(elem!1)), s(s(s(s(s(z)))))) | r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[877, 25])).
% 1.64/1.83 tff(879,plain,
% 1.64/1.83 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[878, 874, 746])).
% 1.64/1.83 tff(880,plain,
% 1.64/1.83 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[879, 738])).
% 1.64/1.83 tff(881,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(882,plain,
% 1.64/1.83 ((s(s(elem!1)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[881])).
% 1.64/1.83 tff(883,plain,
% 1.64/1.83 ((~(s(s(elem!1)) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[882])).
% 1.64/1.83 tff(884,plain,
% 1.64/1.83 (~(s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[746, 883])).
% 1.64/1.83 tff(885,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[705])).
% 1.64/1.83 tff(886,plain,
% 1.64/1.83 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[885])).
% 1.64/1.83 tff(887,plain,
% 1.64/1.83 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[886])).
% 1.64/1.83 tff(888,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[471, 171, 866, 259, 858])).
% 1.64/1.83 tff(889,plain,
% 1.64/1.83 (~b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[888, 887])).
% 1.64/1.83 tff(890,plain,
% 1.64/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(rewrite,[status(thm)],[])).
% 1.64/1.83 tff(891,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.83 inference(quant_inst,[status(thm)],[])).
% 1.64/1.83 tff(892,plain,
% 1.64/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[891, 890])).
% 1.64/1.83 tff(893,plain,
% 1.64/1.83 ((s(s(s(s(s(z))))) = s(s(elem!1))) | b(s(s(s(s(s(z))))), s(s(elem!1))) | r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[892, 25])).
% 1.64/1.83 tff(894,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[893, 889, 884])).
% 1.64/1.83 tff(895,plain,
% 1.64/1.83 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(z)))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[693, 705])).
% 1.64/1.83 tff(896,plain,
% 1.64/1.83 (r(z, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 1.64/1.83 inference(symmetry,[status(thm)],[895])).
% 1.64/1.83 tff(897,plain,
% 1.64/1.83 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 1.64/1.83 inference(commutativity,[status(thm)],[])).
% 1.64/1.83 tff(898,plain,
% 1.64/1.83 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.64/1.83 inference(symmetry,[status(thm)],[897])).
% 1.64/1.83 tff(899,plain,
% 1.64/1.83 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.64/1.83 inference(monotonicity,[status(thm)],[898])).
% 1.64/1.83 tff(900,plain,
% 1.64/1.83 (~(s(s(z)) = s(s(s(z))))),
% 1.64/1.83 inference(modus_ponens,[status(thm)],[80, 899])).
% 1.64/1.83 tff(901,plain,
% 1.64/1.83 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.64/1.83 inference(unit_resolution,[status(thm)],[225, 888])).
% 1.64/1.83 tff(902,plain,
% 1.64/1.84 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.84 tff(903,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[902])).
% 1.64/1.84 tff(904,plain,
% 1.64/1.84 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.84 tff(905,plain,
% 1.64/1.84 ((~r(z, s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[904])).
% 1.64/1.84 tff(906,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(907,plain,
% 1.64/1.84 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(908,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[907])).
% 1.64/1.84 tff(909,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[908, 906])).
% 1.64/1.84 tff(910,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(911,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.64/1.84 tff(912,plain,
% 1.64/1.84 (~r(z, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[911, 106, 96, 95, 747])).
% 1.64/1.84 tff(913,plain,
% 1.64/1.84 (~r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[912, 905])).
% 1.64/1.84 tff(914,plain,
% 1.64/1.84 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.64/1.84 inference(commutativity,[status(thm)],[])).
% 1.64/1.84 tff(915,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(916,plain,
% 1.64/1.84 (inj_0(s(elem!1)) = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[915, 42])).
% 1.64/1.84 tff(917,plain,
% 1.64/1.84 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[710])).
% 1.64/1.84 tff(918,plain,
% 1.64/1.84 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.64/1.84 inference(symmetry,[status(thm)],[917])).
% 1.64/1.84 tff(919,plain,
% 1.64/1.84 (z = inj_0(s(z))),
% 1.64/1.84 inference(symmetry,[status(thm)],[44])).
% 1.64/1.84 tff(920,plain,
% 1.64/1.84 (z = elem!1),
% 1.64/1.84 inference(transitivity,[status(thm)],[919, 918, 916])).
% 1.64/1.84 tff(921,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[695, 920])).
% 1.64/1.84 tff(922,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(923,plain,
% 1.64/1.84 (z = elem!1),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[922, 710])).
% 1.64/1.84 tff(924,plain,
% 1.64/1.84 (elem!1 = z),
% 1.64/1.84 inference(symmetry,[status(thm)],[923])).
% 1.64/1.84 tff(925,plain,
% 1.64/1.84 ((elem!1 = s(s(s(z)))) <=> (z = s(s(s(z))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[924])).
% 1.64/1.84 tff(926,plain,
% 1.64/1.84 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.64/1.84 inference(transitivity,[status(thm)],[925, 914])).
% 1.64/1.84 tff(927,plain,
% 1.64/1.84 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[926])).
% 1.64/1.84 tff(928,plain,
% 1.64/1.84 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[927])).
% 1.64/1.84 tff(929,plain,
% 1.64/1.84 (~(elem!1 = s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[194, 928])).
% 1.64/1.84 tff(930,plain,
% 1.64/1.84 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[712])).
% 1.64/1.84 tff(931,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[930])).
% 1.64/1.84 tff(932,plain,
% 1.64/1.84 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(symmetry,[status(thm)],[931])).
% 1.64/1.84 tff(933,plain,
% 1.64/1.84 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(z)))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[932])).
% 1.64/1.84 tff(934,assumption,(~b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.84 tff(935,plain,
% 1.64/1.84 (~b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[934, 933])).
% 1.64/1.84 tff(936,assumption,(~r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.84 tff(937,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(938,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(939,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[938, 937])).
% 1.64/1.84 tff(940,plain,
% 1.64/1.84 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[939, 25, 936])).
% 1.64/1.84 tff(941,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[940, 935, 929])).
% 1.64/1.84 tff(942,plain,(r(elem!1, s(s(s(z)))) | b(elem!1, s(s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(943,plain,
% 1.64/1.84 (b(elem!1, s(s(s(elem!1))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[942, 913, 704])).
% 1.64/1.84 tff(944,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.84 tff(945,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[944, 932])).
% 1.64/1.84 tff(946,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.84 tff(947,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[946, 945])).
% 1.64/1.84 tff(948,plain,(b(elem!1, s(s(s(z)))) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(949,plain,
% 1.64/1.84 (b(elem!1, s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[948, 943, 704])).
% 1.64/1.84 tff(950,plain,
% 1.64/1.84 (b(z, s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[949, 903])).
% 1.64/1.84 tff(951,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(952,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(953,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[952, 951])).
% 1.64/1.84 tff(954,plain,
% 1.64/1.84 (b(s(s(s(z))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[953, 25, 194, 795])).
% 1.64/1.84 tff(955,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(956,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(957,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[956, 955])).
% 1.64/1.84 tff(958,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[957, 106, 96, 637, 396, 127])).
% 1.64/1.84 tff(959,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(960,plain,
% 1.64/1.84 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[959, 901, 637, 96])).
% 1.64/1.84 tff(961,plain,
% 1.64/1.84 (b(s(s(s(s(s(z))))), z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[143, 25, 140, 960])).
% 1.64/1.84 tff(962,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(963,plain,
% 1.64/1.84 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(964,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[963])).
% 1.64/1.84 tff(965,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[964, 962])).
% 1.64/1.84 tff(966,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(967,plain,
% 1.64/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[966, 965])).
% 1.64/1.84 tff(968,plain,
% 1.64/1.84 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[967, 171, 961, 954, 950])).
% 1.64/1.84 tff(969,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[835, 968, 827])).
% 1.64/1.84 tff(970,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(971,plain,
% 1.64/1.84 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(972,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[971])).
% 1.64/1.84 tff(973,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[972, 970])).
% 1.64/1.84 tff(974,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(975,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[974, 973])).
% 1.64/1.84 tff(976,plain,
% 1.64/1.84 (~r(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[975, 106, 969, 901, 880])).
% 1.64/1.84 tff(977,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(978,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(979,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[978, 977])).
% 1.64/1.84 tff(980,plain,
% 1.64/1.84 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[979, 25, 976])).
% 1.64/1.84 tff(981,plain,
% 1.64/1.84 (b(s(s(z)), s(s(s(z))))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[980, 900])).
% 1.64/1.84 tff(982,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(983,plain,
% 1.64/1.84 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(984,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[983])).
% 1.64/1.84 tff(985,plain,
% 1.64/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.84 inference(transitivity,[status(thm)],[984, 982])).
% 1.64/1.84 tff(986,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(987,plain,
% 1.64/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[986, 985])).
% 1.64/1.84 tff(988,plain,
% 1.64/1.84 (~r(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[987, 106, 969, 901, 880])).
% 1.64/1.84 tff(989,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[930])).
% 1.64/1.84 tff(990,plain,
% 1.64/1.84 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[989])).
% 1.64/1.84 tff(991,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(992,plain,
% 1.64/1.84 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[991, 990])).
% 1.64/1.84 tff(993,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(994,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[993, 992])).
% 1.64/1.84 tff(995,plain,(r(s(s(s(z))), s(s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(996,plain,
% 1.64/1.84 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[995, 988, 704])).
% 1.64/1.84 tff(997,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.64/1.84 tff(998,plain,
% 1.64/1.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[997])).
% 1.64/1.84 tff(999,plain,
% 1.64/1.84 (s(s(elem!1)) = s(z)),
% 1.64/1.84 inference(transitivity,[status(thm)],[813, 998, 70])).
% 1.64/1.84 tff(1000,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[999])).
% 1.64/1.84 tff(1001,plain,
% 1.64/1.84 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1002,plain,
% 1.64/1.84 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1001, 42])).
% 1.64/1.84 tff(1003,plain,
% 1.64/1.84 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.64/1.84 inference(symmetry,[status(thm)],[1002])).
% 1.64/1.84 tff(1004,plain,
% 1.64/1.84 (s(elem!1) = z),
% 1.64/1.84 inference(transitivity,[status(thm)],[1003, 1000, 44])).
% 1.64/1.84 tff(1005,plain,
% 1.64/1.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1006,plain,
% 1.64/1.84 (~(s(elem!1) = z)),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1005, 13])).
% 1.64/1.84 tff(1007,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1006, 1004])).
% 1.64/1.84 tff(1008,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1009,plain,
% 1.64/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1010,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.64/1.84 inference(quant_inst,[status(thm)],[])).
% 1.64/1.84 tff(1011,plain,
% 1.64/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1010, 1009])).
% 1.64/1.84 tff(1012,plain,
% 1.64/1.84 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1011, 25])).
% 1.64/1.84 tff(1013,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1012, 1008])).
% 1.64/1.84 tff(1014,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1013, 996])).
% 1.64/1.84 tff(1015,plain,
% 1.64/1.84 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[712])).
% 1.64/1.84 tff(1016,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(1017,plain,
% 1.64/1.84 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(modus_ponens,[status(thm)],[1016, 1015])).
% 1.64/1.84 tff(1018,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.64/1.84 tff(1019,plain,
% 1.64/1.84 ($false),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1018, 1017])).
% 1.64/1.84 tff(1020,plain,((~b(s(s(s(elem!1))), s(s(z)))) | b(s(s(s(z))), s(s(z))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.84 tff(1021,plain,
% 1.64/1.84 (b(s(s(s(z))), s(s(z)))),
% 1.64/1.84 inference(unit_resolution,[status(thm)],[1020, 1014, 704])).
% 1.64/1.84 tff(1022,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1023,plain,
% 1.64/1.84 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), 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(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.64/1.84 inference(rewrite,[status(thm)],[])).
% 1.64/1.84 tff(1024,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.64/1.84 inference(monotonicity,[status(thm)],[1023])).
% 1.64/1.84 tff(1025,plain,
% 1.64/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1024, 1022])).
% 1.64/1.85 tff(1026,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1027,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1026, 1025])).
% 1.64/1.85 tff(1028,plain,
% 1.64/1.85 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1027, 171, 259, 1021, 950])).
% 1.64/1.85 tff(1029,plain,
% 1.64/1.85 (~b(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1028, 981])).
% 1.64/1.85 tff(1030,plain,
% 1.64/1.85 (r(z, s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[124, 1029])).
% 1.64/1.85 tff(1031,plain,
% 1.64/1.85 (r(elem!1, s(s(elem!1)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1030, 896])).
% 1.64/1.85 tff(1032,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1033,plain,
% 1.64/1.85 (((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1034,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1033])).
% 1.64/1.85 tff(1035,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1034, 1032])).
% 1.64/1.85 tff(1036,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(elem!1)))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1037,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1036, 1035])).
% 1.64/1.85 tff(1038,plain,
% 1.64/1.85 ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1037, 106])).
% 1.64/1.85 tff(1039,plain,
% 1.64/1.85 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1038, 1031, 894, 879])).
% 1.64/1.85 tff(1040,plain,
% 1.64/1.85 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[782, 1039, 768])).
% 1.64/1.85 tff(1041,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.85 tff(1042,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[1041])).
% 1.64/1.85 tff(1043,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(1044,plain,
% 1.64/1.85 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(symmetry,[status(thm)],[1043])).
% 1.64/1.85 tff(1045,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.85 tff(1046,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1045, 1043])).
% 1.64/1.85 tff(1047,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(transitivity,[status(thm)],[1046, 1044])).
% 1.64/1.85 tff(1048,plain,
% 1.64/1.85 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1047])).
% 1.64/1.85 tff(1049,plain,
% 1.64/1.85 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1050,plain,
% 1.64/1.85 (~(s(s(s(s(elem!1)))) = z)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1049, 13])).
% 1.64/1.85 tff(1051,plain,
% 1.64/1.85 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1050, 1048])).
% 1.64/1.85 tff(1052,plain,
% 1.64/1.85 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[705])).
% 1.64/1.85 tff(1053,plain,
% 1.64/1.85 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1052])).
% 1.64/1.85 tff(1054,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1053])).
% 1.64/1.85 tff(1055,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(symmetry,[status(thm)],[1054])).
% 1.64/1.85 tff(1056,plain,
% 1.64/1.85 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1055])).
% 1.64/1.85 tff(1057,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1053])).
% 1.64/1.85 tff(1058,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1053])).
% 1.64/1.85 tff(1059,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1058])).
% 1.64/1.85 tff(1060,plain,
% 1.64/1.85 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1059])).
% 1.64/1.85 tff(1061,plain,
% 1.64/1.85 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[315, 1060])).
% 1.64/1.85 tff(1062,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1063,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1064,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1063, 1062])).
% 1.64/1.85 tff(1065,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1064, 25])).
% 1.64/1.85 tff(1066,plain,
% 1.64/1.85 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1065, 726])).
% 1.64/1.85 tff(1067,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1066, 1061])).
% 1.64/1.85 tff(1068,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1067, 1057])).
% 1.64/1.85 tff(1069,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1070,plain,
% 1.64/1.85 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1071,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1070])).
% 1.64/1.85 tff(1072,plain,
% 1.64/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1071, 1069])).
% 1.64/1.85 tff(1073,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1074,plain,
% 1.64/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1073, 1072])).
% 1.64/1.85 tff(1075,plain,
% 1.64/1.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1074, 106, 95, 1068, 747])).
% 1.64/1.85 tff(1076,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.64/1.85 tff(1077,plain,
% 1.64/1.85 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1076])).
% 1.64/1.85 tff(1078,plain,
% 1.64/1.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1077])).
% 1.64/1.85 tff(1079,plain,
% 1.64/1.85 (s(s(s(s(z)))) = s(s(s(z)))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1076])).
% 1.64/1.85 tff(1080,plain,
% 1.64/1.85 (s(s(s(s(z)))) = s(s(z))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1079, 191, 1078, 65])).
% 1.64/1.85 tff(1081,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[369, 1080])).
% 1.64/1.85 tff(1082,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1083,plain,
% 1.64/1.85 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1082, 821])).
% 1.64/1.85 tff(1084,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.85 tff(1085,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(symmetry,[status(thm)],[1084])).
% 1.64/1.85 tff(1086,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(1087,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 1.64/1.85 tff(1088,plain,
% 1.64/1.85 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[761])).
% 1.64/1.85 tff(1089,plain,
% 1.64/1.85 (b(elem!1, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1088])).
% 1.64/1.85 tff(1090,plain,
% 1.64/1.85 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[840, 1089])).
% 1.64/1.85 tff(1091,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.64/1.85 tff(1092,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1093,plain,
% 1.64/1.85 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1094,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1093])).
% 1.64/1.85 tff(1095,plain,
% 1.64/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1094, 1092])).
% 1.64/1.85 tff(1096,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1097,plain,
% 1.64/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.64/1.85 tff(1098,plain,
% 1.64/1.85 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1097, 171, 159, 1091])).
% 1.64/1.85 tff(1099,plain,
% 1.64/1.85 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1098, 1090, 1087])).
% 1.64/1.85 tff(1100,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1101,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1102,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.64/1.85 tff(1103,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1102, 25, 1099, 1083, 1075])).
% 1.64/1.85 tff(1104,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~(elem!1 = z)) | (~b(elem!1, s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1105,plain,
% 1.64/1.85 (~b(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1104, 315, 747, 159, 954, 693, 840, 95])).
% 1.64/1.85 tff(1106,plain,
% 1.64/1.85 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1105, 1056])).
% 1.64/1.85 tff(1107,plain,
% 1.64/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.85 inference(rewrite,[status(thm)],[])).
% 1.64/1.85 tff(1108,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.64/1.85 inference(quant_inst,[status(thm)],[])).
% 1.64/1.85 tff(1109,plain,
% 1.64/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1108, 1107])).
% 1.64/1.85 tff(1110,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1109, 25])).
% 1.64/1.85 tff(1111,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1110, 1106, 1051])).
% 1.64/1.85 tff(1112,plain,
% 1.64/1.85 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(monotonicity,[status(thm)],[713])).
% 1.64/1.85 tff(1113,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(1114,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.64/1.85 tff(1115,assumption,(~r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.64/1.85 tff(1116,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1115, 1114])).
% 1.64/1.85 tff(1117,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | r(s(s(s(s(z)))), elem!1) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1118,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), elem!1)),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1117, 1111, 704])).
% 1.64/1.85 tff(1119,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), z)),
% 1.64/1.85 inference(modus_ponens,[status(thm)],[1118, 1042])).
% 1.64/1.85 tff(1120,plain,
% 1.64/1.85 ($false),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[266, 106, 96, 95, 1068, 1119])).
% 1.64/1.85 tff(1121,plain,(b(s(s(s(s(z)))), s(z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~(elem!1 = z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.85 tff(1122,plain,
% 1.64/1.85 (b(s(s(s(s(z)))), s(z))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[1121, 747, 95, 693, 96, 961, 1040])).
% 1.64/1.85 tff(1123,plain,
% 1.64/1.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[363, 171, 866, 259, 1122])).
% 1.64/1.85 tff(1124,plain,
% 1.64/1.85 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.85 inference(unit_resolution,[status(thm)],[372, 25, 821, 1123])).
% 1.64/1.85 tff(1125,plain,
% 1.64/1.85 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(commutativity,[status(thm)],[])).
% 1.64/1.85 tff(1126,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.64/1.85 inference(monotonicity,[status(thm)],[1053, 1052])).
% 1.64/1.85 tff(1127,plain,
% 1.64/1.85 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.85 inference(transitivity,[status(thm)],[1126, 1125])).
% 1.64/1.85 tff(1128,plain,
% 1.64/1.85 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.85 inference(symmetry,[status(thm)],[1127])).
% 1.64/1.85 tff(1129,plain,
% 1.64/1.85 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1128])).
% 1.64/1.86 tff(1130,plain,
% 1.64/1.86 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1083, 1129])).
% 1.64/1.86 tff(1131,plain,
% 1.64/1.86 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(s(z)))))),
% 1.64/1.86 inference(symmetry,[status(thm)],[405])).
% 1.64/1.86 tff(1132,plain,
% 1.64/1.86 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.64/1.86 inference(transitivity,[status(thm)],[713, 49, 1131, 190, 930])).
% 1.64/1.86 tff(1133,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.86 tff(1134,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1133, 1132])).
% 1.64/1.86 tff(1135,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1136,plain,
% 1.64/1.86 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1135, 1130, 704])).
% 1.64/1.86 tff(1137,plain,
% 1.64/1.86 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[421, 1136])).
% 1.64/1.86 tff(1138,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1139,plain,
% 1.64/1.86 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1140,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1139])).
% 1.64/1.86 tff(1141,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1140, 1138])).
% 1.64/1.86 tff(1142,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1143,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1142, 1141])).
% 1.64/1.86 tff(1144,plain,
% 1.64/1.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1143, 171, 866, 259, 858, 1122])).
% 1.64/1.86 tff(1145,plain,
% 1.64/1.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[426, 1144, 1137])).
% 1.64/1.86 tff(1146,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1147,plain,
% 1.64/1.86 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1148,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1147])).
% 1.64/1.86 tff(1149,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1148, 1146])).
% 1.64/1.86 tff(1150,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1151,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1150, 1149])).
% 1.64/1.86 tff(1152,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1151, 171, 866, 259, 858, 1122])).
% 1.64/1.86 tff(1153,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1154,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1155,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 1.64/1.86 tff(1156,plain,
% 1.64/1.86 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) | b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1155, 25])).
% 1.64/1.86 tff(1157,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1156, 1152, 1136])).
% 1.64/1.86 tff(1158,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1159,plain,
% 1.64/1.86 (((~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(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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1160,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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)))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1159])).
% 1.64/1.86 tff(1161,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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))))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1160, 1158])).
% 1.64/1.86 tff(1162,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1163,plain,
% 1.64/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 1.64/1.86 tff(1164,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1163, 106, 1157, 1145, 1124, 880])).
% 1.64/1.86 tff(1165,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~(elem!1 = z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1166,plain,
% 1.64/1.86 (~r(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1165, 693, 95, 259, 96, 735, 730])).
% 1.64/1.86 tff(1167,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.64/1.86 tff(1168,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.64/1.86 tff(1169,plain,
% 1.64/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1170,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1171,plain,
% 1.64/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1170, 1169])).
% 1.64/1.86 tff(1172,plain,
% 1.64/1.86 ($false),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1171, 25, 1168, 344, 1167])).
% 1.64/1.86 tff(1173,plain,(r(s(s(s(z))), s(z)) | b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.86 tff(1174,plain,
% 1.64/1.86 (b(s(s(s(z))), s(z))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1173, 1166])).
% 1.64/1.86 tff(1175,plain,
% 1.64/1.86 (~r(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[864, 106, 96, 735, 95])).
% 1.64/1.86 tff(1176,plain,
% 1.64/1.86 (b(s(z), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[550, 1175])).
% 1.64/1.86 tff(1177,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1178,plain,
% 1.64/1.86 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1179,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1178])).
% 1.64/1.86 tff(1180,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1179, 1177])).
% 1.64/1.86 tff(1181,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1182,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 1.64/1.86 tff(1183,plain,
% 1.64/1.86 (~b(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1182, 171, 1176, 259, 1174])).
% 1.64/1.86 tff(1184,plain,
% 1.64/1.86 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1020, 1183, 704])).
% 1.64/1.86 tff(1185,plain,
% 1.64/1.86 (r(s(s(s(elem!1))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1013, 1184])).
% 1.64/1.86 tff(1186,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[995, 1185, 704])).
% 1.64/1.86 tff(1187,plain,
% 1.64/1.86 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1082, 369])).
% 1.64/1.86 tff(1188,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.64/1.86 tff(1189,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1190,plain,
% 1.64/1.86 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(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(s(s(s(z)))))))),
% 1.64/1.86 inference(rewrite,[status(thm)],[])).
% 1.64/1.86 tff(1191,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.64/1.86 inference(monotonicity,[status(thm)],[1190])).
% 1.64/1.86 tff(1192,plain,
% 1.64/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(transitivity,[status(thm)],[1191, 1189])).
% 1.64/1.86 tff(1193,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.86 inference(quant_inst,[status(thm)],[])).
% 1.64/1.86 tff(1194,plain,
% 1.64/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.64/1.86 inference(modus_ponens,[status(thm)],[1193, 1192])).
% 1.64/1.86 tff(1195,plain,
% 1.64/1.86 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1194, 171, 323, 259, 1188, 357])).
% 1.64/1.86 tff(1196,plain,
% 1.64/1.86 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[1102, 25, 1195, 1187])).
% 1.64/1.86 tff(1197,plain,
% 1.64/1.86 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[363, 171, 323, 259, 357])).
% 1.64/1.86 tff(1198,plain,
% 1.64/1.86 (r(s(s(s(s(z)))), s(s(z)))),
% 1.64/1.86 inference(unit_resolution,[status(thm)],[372, 25, 369, 1197])).
% 1.64/1.86 tff(1199,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.64/1.86 tff(1200,plain,
% 1.64/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1201,plain,
% 1.64/1.87 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1202,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1201])).
% 1.64/1.87 tff(1203,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1202, 1200])).
% 1.64/1.87 tff(1204,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1205,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 1.64/1.87 tff(1206,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1205, 106, 637, 1199, 1198, 1196])).
% 1.64/1.87 tff(1207,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(s(z)))) = s(s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1208,plain,
% 1.64/1.87 (~b(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1207, 735, 1186, 821, 1176, 259, 1174])).
% 1.64/1.87 tff(1209,plain,
% 1.64/1.87 (r(s(s(s(s(z)))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[321, 1208, 729])).
% 1.64/1.87 tff(1210,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1052])).
% 1.64/1.87 tff(1211,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[1210])).
% 1.64/1.87 tff(1212,plain,
% 1.64/1.87 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1211])).
% 1.64/1.87 tff(1213,plain,
% 1.64/1.87 (~r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[777, 769, 95, 730])).
% 1.64/1.87 tff(1214,plain,
% 1.64/1.87 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[479, 1213])).
% 1.64/1.87 tff(1215,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1216,plain,
% 1.64/1.87 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1217,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1216])).
% 1.64/1.87 tff(1218,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1217, 1215])).
% 1.64/1.87 tff(1219,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1220,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 1.64/1.87 tff(1221,plain,
% 1.64/1.87 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1220, 171, 323, 259, 1188, 1214])).
% 1.64/1.87 tff(1222,plain,
% 1.64/1.87 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1221, 1212])).
% 1.64/1.87 tff(1223,plain,
% 1.64/1.87 ((s(s(s(s(s(z))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.64/1.87 inference(commutativity,[status(thm)],[])).
% 1.64/1.87 tff(1224,plain,
% 1.64/1.87 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1052])).
% 1.64/1.87 tff(1225,plain,
% 1.64/1.87 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1224, 1223])).
% 1.64/1.87 tff(1226,plain,
% 1.64/1.87 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[1225])).
% 1.64/1.87 tff(1227,plain,
% 1.64/1.87 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = s(s(s(elem!1)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1226])).
% 1.64/1.87 tff(1228,plain,
% 1.64/1.87 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[827, 1227])).
% 1.64/1.87 tff(1229,plain,
% 1.64/1.87 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[693])).
% 1.64/1.87 tff(1230,plain,
% 1.64/1.87 (r(z, s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[769, 1229])).
% 1.64/1.87 tff(1231,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1232,plain,
% 1.64/1.87 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1233,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1232])).
% 1.64/1.87 tff(1234,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1233, 1231])).
% 1.64/1.87 tff(1235,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1236,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1235, 1234])).
% 1.64/1.87 tff(1237,plain,
% 1.64/1.87 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1236, 171, 323, 259, 1188, 1214])).
% 1.64/1.87 tff(1238,plain,
% 1.64/1.87 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[835, 1237, 827])).
% 1.64/1.87 tff(1239,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[736])).
% 1.64/1.87 tff(1240,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1241,plain,
% 1.64/1.87 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1242,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1241])).
% 1.64/1.87 tff(1243,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1242, 1240])).
% 1.64/1.87 tff(1244,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1245,plain,
% 1.64/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1244, 1243])).
% 1.64/1.87 tff(1246,plain,
% 1.64/1.87 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1245, 171, 323, 259, 1188])).
% 1.64/1.87 tff(1247,plain,
% 1.64/1.87 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[979, 25, 1246])).
% 1.64/1.87 tff(1248,plain,
% 1.64/1.87 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1247, 900])).
% 1.64/1.87 tff(1249,plain,
% 1.64/1.87 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1248, 1239])).
% 1.64/1.87 tff(1250,assumption,(s(s(s(s(s(z))))) = s(s(s(z)))), introduced(assumption)).
% 1.64/1.87 tff(1251,plain,
% 1.64/1.87 (s(s(s(z))) = s(s(s(s(s(z)))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1250, 1223])).
% 1.64/1.87 tff(1252,assumption,(~(s(s(s(z))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.87 tff(1253,plain,
% 1.64/1.87 ($false),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1252, 1251])).
% 1.64/1.87 tff(1254,plain,((~(s(s(s(s(s(z))))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.87 tff(1255,plain,
% 1.64/1.87 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1254, 827])).
% 1.64/1.87 tff(1256,plain,
% 1.64/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1257,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1258,plain,
% 1.64/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1257, 1256])).
% 1.64/1.87 tff(1259,plain,
% 1.64/1.87 ((s(s(s(s(s(z))))) = s(s(s(z)))) | b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1258, 25])).
% 1.64/1.87 tff(1260,plain,
% 1.64/1.87 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1259, 1221, 1255])).
% 1.64/1.87 tff(1261,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1262,plain,
% 1.64/1.87 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(rewrite,[status(thm)],[])).
% 1.64/1.87 tff(1263,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1262])).
% 1.64/1.87 tff(1264,plain,
% 1.64/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.64/1.87 inference(transitivity,[status(thm)],[1263, 1261])).
% 1.64/1.87 tff(1265,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 1.64/1.87 inference(quant_inst,[status(thm)],[])).
% 1.64/1.87 tff(1266,plain,
% 1.64/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1265, 1264])).
% 1.64/1.87 tff(1267,plain,
% 1.64/1.87 ((~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1266, 106])).
% 1.64/1.87 tff(1268,plain,
% 1.64/1.87 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[1267, 1260, 1249, 1238])).
% 1.64/1.87 tff(1269,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(unit_resolution,[status(thm)],[878, 1268, 746])).
% 1.64/1.87 tff(1270,plain,
% 1.64/1.87 (s(s(z)) = s(s(elem!1))),
% 1.64/1.87 inference(symmetry,[status(thm)],[711])).
% 1.64/1.87 tff(1271,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(monotonicity,[status(thm)],[1270])).
% 1.64/1.87 tff(1272,plain,
% 1.64/1.87 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(symmetry,[status(thm)],[1271])).
% 1.64/1.87 tff(1273,assumption,(b(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.87 tff(1274,plain,
% 1.64/1.87 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.87 inference(modus_ponens,[status(thm)],[1273, 1272])).
% 1.64/1.87 tff(1275,assumption,(b(s(z), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.87 tff(1276,plain,
% 1.64/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1277,plain,
% 1.64/1.88 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1278,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1277])).
% 1.64/1.88 tff(1279,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1278, 1276])).
% 1.64/1.88 tff(1280,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1281,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1280, 1279])).
% 1.64/1.88 tff(1282,plain,
% 1.64/1.88 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1281, 171, 323, 1275, 4])).
% 1.64/1.88 tff(1283,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1282, 1274])).
% 1.64/1.88 tff(1284,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1285,plain,
% 1.64/1.88 (~b(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1284, 1269, 323, 1214, 704])).
% 1.64/1.88 tff(1286,plain,
% 1.64/1.88 (r(s(z), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[60, 1285])).
% 1.64/1.88 tff(1287,assumption,(r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.88 tff(1288,assumption,(r(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.88 tff(1289,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1290,plain,
% 1.64/1.88 (((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1291,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1290])).
% 1.64/1.88 tff(1292,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1291, 1289])).
% 1.64/1.88 tff(1293,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1294,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 1.64/1.88 tff(1295,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1294, 106, 95, 126, 1288, 1287])).
% 1.64/1.88 tff(1296,plain,((~r(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1297,plain,
% 1.64/1.88 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1296, 1286, 1230, 95])).
% 1.64/1.88 tff(1298,assumption,(~r(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.88 tff(1299,assumption,(~b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.88 tff(1300,assumption,(~(s(s(s(s(s(z))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.64/1.88 tff(1301,plain,
% 1.64/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1302,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1303,plain,
% 1.64/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1302, 1301])).
% 1.64/1.88 tff(1304,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1303, 25, 1300, 1299, 1298])).
% 1.64/1.88 tff(1305,plain,(b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1306,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1305, 1297, 1228])).
% 1.64/1.88 tff(1307,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1306, 1222])).
% 1.64/1.88 tff(1308,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~(elem!1 = z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1309,plain,
% 1.64/1.88 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1308, 1176, 95, 259, 1174, 693, 730])).
% 1.64/1.88 tff(1310,plain,
% 1.64/1.88 (b(elem!1, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[782, 1309, 768])).
% 1.64/1.88 tff(1311,plain,
% 1.64/1.88 (b(z, s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1310, 1089])).
% 1.64/1.88 tff(1312,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[272, 25, 52, 267])).
% 1.64/1.88 tff(1313,assumption,(b(z, s(s(s(s(s(z))))))), introduced(assumption)).
% 1.64/1.88 tff(1314,plain,
% 1.64/1.88 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[421, 419])).
% 1.64/1.88 tff(1315,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1316,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1317,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1316, 1315])).
% 1.64/1.88 tff(1318,plain,
% 1.64/1.88 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1317, 106, 95, 502, 263])).
% 1.64/1.88 tff(1319,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[426, 1318, 1314])).
% 1.64/1.88 tff(1320,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1321,plain,
% 1.64/1.88 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1322,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1321])).
% 1.64/1.88 tff(1323,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1322, 1320])).
% 1.64/1.88 tff(1324,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1325,plain,
% 1.64/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 1.64/1.88 tff(1326,plain,
% 1.64/1.88 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1325, 106, 95, 502, 263])).
% 1.64/1.88 tff(1327,plain,
% 1.64/1.88 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1156, 1326, 419])).
% 1.64/1.88 tff(1328,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1329,plain,
% 1.64/1.88 (((~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(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1330,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1329])).
% 1.64/1.88 tff(1331,plain,
% 1.64/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.64/1.88 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.64/1.88 tff(1332,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.64/1.88 inference(quant_inst,[status(thm)],[])).
% 1.64/1.88 tff(1333,plain,
% 1.64/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.64/1.88 tff(1334,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1333, 171, 1327, 1319, 1313, 1312])).
% 1.64/1.88 tff(1335,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1336,plain,
% 1.64/1.88 (~r(s(s(s(s(s(z))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1335, 1311, 1136, 95, 1209, 96])).
% 1.64/1.88 tff(1337,plain,
% 1.64/1.88 (b(s(s(s(s(s(z))))), s(z))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[479, 1336])).
% 1.64/1.88 tff(1338,plain,
% 1.64/1.88 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[872, 171, 1176, 259, 1337])).
% 1.64/1.88 tff(1339,plain,
% 1.64/1.88 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1338, 708])).
% 1.64/1.88 tff(1340,plain,
% 1.64/1.88 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1236, 171, 1176, 259, 1174, 1337])).
% 1.64/1.88 tff(1341,plain,
% 1.64/1.88 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[835, 1340, 827])).
% 1.64/1.88 tff(1342,plain,
% 1.64/1.88 (~b(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1245, 171, 1176, 259, 1174])).
% 1.64/1.88 tff(1343,plain,
% 1.64/1.88 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[979, 25, 1342])).
% 1.64/1.88 tff(1344,plain,
% 1.64/1.88 (r(s(s(z)), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1343, 900])).
% 1.64/1.88 tff(1345,plain,
% 1.64/1.88 (r(s(s(elem!1)), s(s(s(z))))),
% 1.64/1.88 inference(modus_ponens,[status(thm)],[1344, 1239])).
% 1.64/1.88 tff(1346,plain,
% 1.64/1.88 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1220, 171, 1176, 259, 1174, 1337])).
% 1.64/1.88 tff(1347,plain,
% 1.64/1.88 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1259, 1346, 1255])).
% 1.64/1.88 tff(1348,plain,
% 1.64/1.88 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1267, 1347, 1345, 1341])).
% 1.64/1.88 tff(1349,plain,
% 1.64/1.88 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[878, 1348, 746])).
% 1.64/1.88 tff(1350,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1349, 1339])).
% 1.64/1.88 tff(1351,plain,((~(elem!1 = z)) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(elem!1, s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1352,plain,
% 1.64/1.88 (~(elem!1 = z)),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1351, 692, 94, 259, 95, 670])).
% 1.64/1.88 tff(1353,plain,
% 1.64/1.88 ($false),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1352, 653])).
% 1.64/1.88 tff(1354,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | b(z, s(z)) | b(z, elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.88 tff(1355,plain,
% 1.64/1.88 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[1354, 260, 95, 84, 258, 83, 126, 259])).
% 1.64/1.88 tff(1356,plain,
% 1.64/1.88 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.64/1.88 inference(unit_resolution,[status(thm)],[205, 1355])).
% 1.64/1.88 tff(1357,assumption,(r(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.64/1.88 tff(1358,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1359,plain,
% 1.64/1.88 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.88 inference(rewrite,[status(thm)],[])).
% 1.64/1.88 tff(1360,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.64/1.88 inference(monotonicity,[status(thm)],[1359])).
% 1.64/1.88 tff(1361,plain,
% 1.64/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1360, 1358])).
% 1.64/1.89 tff(1362,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1363,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1362, 1361])).
% 1.64/1.89 tff(1364,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1363, 106, 260, 126, 1357, 3])).
% 1.64/1.89 tff(1365,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1366,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1365, 612, 126, 260])).
% 1.64/1.89 tff(1367,plain,
% 1.64/1.89 (~(s(s(s(s(s(z))))) = s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1254, 413])).
% 1.64/1.89 tff(1368,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(z)))) | r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1259, 1367])).
% 1.64/1.89 tff(1369,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1368, 1366])).
% 1.64/1.89 tff(1370,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1371,plain,
% 1.64/1.89 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1372,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1371])).
% 1.64/1.89 tff(1373,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1372, 1370])).
% 1.64/1.89 tff(1374,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1375,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1374, 1373])).
% 1.64/1.89 tff(1376,plain,
% 1.64/1.89 ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1375, 106])).
% 1.64/1.89 tff(1377,plain,
% 1.64/1.89 (~r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1376, 730, 96, 95])).
% 1.64/1.89 tff(1378,plain,
% 1.64/1.89 (z = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[651, 1377, 258])).
% 1.64/1.89 tff(1379,plain,
% 1.64/1.89 (elem!1 = z),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1378, 262])).
% 1.64/1.89 tff(1380,plain,
% 1.64/1.89 (~(elem!1 = z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1351, 730, 96, 259, 95, 733])).
% 1.64/1.89 tff(1381,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1380, 1379])).
% 1.64/1.89 tff(1382,plain,((~r(elem!1, s(z))) | b(z, elem!1) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1383,plain,
% 1.64/1.89 (~r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1382, 733, 94, 259, 95, 258])).
% 1.64/1.89 tff(1384,assumption,(b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 1.64/1.89 tff(1385,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(1386,plain,
% 1.64/1.89 (r(s(z), s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[550, 1385])).
% 1.64/1.89 tff(1387,plain,
% 1.64/1.89 (~(z = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[691, 1383, 84])).
% 1.64/1.89 tff(1388,plain,
% 1.64/1.89 (r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[651, 1387, 258])).
% 1.64/1.89 tff(1389,plain,
% 1.64/1.89 (~r(s(s(z)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[646, 1388, 1386, 95])).
% 1.64/1.89 tff(1390,plain,
% 1.64/1.89 (b(s(s(z)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[157, 1389])).
% 1.64/1.89 tff(1391,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1392,plain,
% 1.64/1.89 (((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1393,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1392])).
% 1.64/1.89 tff(1394,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1393, 1391])).
% 1.64/1.89 tff(1395,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1396,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1395, 1394])).
% 1.64/1.89 tff(1397,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1396, 106, 638, 95, 126, 127])).
% 1.64/1.89 tff(1398,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1399,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1398, 1388, 95, 126])).
% 1.64/1.89 tff(1400,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[145, 1399])).
% 1.64/1.89 tff(1401,plain,
% 1.64/1.89 (~b(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[215, 1400, 207, 1390])).
% 1.64/1.89 tff(1402,plain,
% 1.64/1.89 (r(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[124, 1401])).
% 1.64/1.89 tff(1403,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1404,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1405,plain,
% 1.64/1.89 (((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1406,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1405])).
% 1.64/1.89 tff(1407,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1406, 1404])).
% 1.64/1.89 tff(1408,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1409,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 1.64/1.89 tff(1410,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1409, 106, 554, 96, 1403, 600])).
% 1.64/1.89 tff(1411,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1412,plain,
% 1.64/1.89 (~r(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1411, 1402, 94, 1386])).
% 1.64/1.89 tff(1413,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1414,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1415,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1414, 1413])).
% 1.64/1.89 tff(1416,plain,
% 1.64/1.89 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1415, 25])).
% 1.64/1.89 tff(1417,plain,
% 1.64/1.89 (s(s(z)) = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1416, 1412, 733])).
% 1.64/1.89 tff(1418,assumption,(s(s(z)) = elem!1), introduced(assumption)).
% 1.64/1.89 tff(1419,plain,
% 1.64/1.89 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1418])).
% 1.64/1.89 tff(1420,plain,
% 1.64/1.89 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1419])).
% 1.64/1.89 tff(1421,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1422,plain,
% 1.64/1.89 (b(s(z), s(s(z)))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1421, 1420])).
% 1.64/1.89 tff(1423,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1385, 1422])).
% 1.64/1.89 tff(1424,plain,((~(s(s(z)) = elem!1)) | b(s(z), s(s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1425,plain,
% 1.64/1.89 (~b(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1424, 1417, 1385])).
% 1.64/1.89 tff(1426,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.64/1.89 tff(1427,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1428,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.64/1.89 tff(1429,plain,
% 1.64/1.89 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(z))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1428])).
% 1.64/1.89 tff(1430,plain,
% 1.64/1.89 (b(s(s(z)), s(z)) <=> b(s(s(z)), elem!1)),
% 1.64/1.89 inference(symmetry,[status(thm)],[1429])).
% 1.64/1.89 tff(1431,plain,
% 1.64/1.89 (b(s(s(z)), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[259, 1430])).
% 1.64/1.89 tff(1432,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[733, 1431])).
% 1.64/1.89 tff(1433,plain,((~(elem!1 = s(z))) | b(s(s(z)), elem!1) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1434,plain,
% 1.64/1.89 (~(elem!1 = s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1433, 733, 259])).
% 1.64/1.89 tff(1435,assumption,(s(z) = elem!1), introduced(assumption)).
% 1.64/1.89 tff(1436,plain,
% 1.64/1.89 (elem!1 = s(z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1435, 671])).
% 1.64/1.89 tff(1437,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 1.64/1.89 tff(1438,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1437, 1436])).
% 1.64/1.89 tff(1439,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1440,plain,
% 1.64/1.89 (~(s(z) = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1439, 1434])).
% 1.64/1.89 tff(1441,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1442,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1443,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 1.64/1.89 tff(1444,plain,
% 1.64/1.89 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1443, 25])).
% 1.64/1.89 tff(1445,plain,
% 1.64/1.89 (r(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1444, 1440, 1427])).
% 1.64/1.89 tff(1446,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1447,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1448,plain,
% 1.64/1.89 (((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1449,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1448])).
% 1.64/1.89 tff(1450,plain,
% 1.64/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1449, 1447])).
% 1.64/1.89 tff(1451,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1452,plain,
% 1.64/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z)))))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1451, 1450])).
% 1.64/1.89 tff(1453,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1452, 106, 638, 95, 1446, 1426])).
% 1.64/1.89 tff(1454,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1455,plain,
% 1.64/1.89 (~r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1454, 1445, 95, 1426])).
% 1.64/1.89 tff(1456,plain,
% 1.64/1.89 (z = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[651, 1455, 258])).
% 1.64/1.89 tff(1457,plain,
% 1.64/1.89 (elem!1 = z),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1456, 262])).
% 1.64/1.89 tff(1458,plain,
% 1.64/1.89 (r(elem!1, s(z))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[691, 1456, 84])).
% 1.64/1.89 tff(1459,plain,
% 1.64/1.89 (~(elem!1 = z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1351, 1458, 94, 259, 95, 733])).
% 1.64/1.89 tff(1460,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1459, 1457])).
% 1.64/1.89 tff(1461,plain,(b(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | b(z, s(z)) | b(z, elem!1) | (~r(elem!1, s(s(s(z))))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1462,plain,
% 1.64/1.89 (~r(elem!1, s(s(s(z))))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1461, 1425, 95, 84, 258, 259, 733])).
% 1.64/1.89 tff(1463,plain,
% 1.64/1.89 (r(s(z), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1444, 1425, 1440])).
% 1.64/1.89 tff(1464,plain,
% 1.64/1.89 (~(z = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[691, 676, 84])).
% 1.64/1.89 tff(1465,plain,
% 1.64/1.89 (r(z, elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[651, 1464, 258])).
% 1.64/1.89 tff(1466,plain,
% 1.64/1.89 (~r(s(s(z)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[646, 1465, 554, 95])).
% 1.64/1.89 tff(1467,plain,
% 1.64/1.89 (b(s(s(z)), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[157, 1466])).
% 1.64/1.89 tff(1468,plain,
% 1.64/1.89 (~r(s(s(s(s(s(z))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1398, 1465, 95, 126])).
% 1.64/1.89 tff(1469,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), z)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[145, 1468])).
% 1.64/1.89 tff(1470,plain,
% 1.64/1.89 (~b(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[215, 1469, 207, 1467])).
% 1.64/1.89 tff(1471,plain,
% 1.64/1.89 (r(z, s(s(z)))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[124, 1470])).
% 1.64/1.89 tff(1472,plain,
% 1.64/1.89 (~r(s(s(z)), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1411, 1471, 94, 554])).
% 1.64/1.89 tff(1473,plain,
% 1.64/1.89 (s(s(z)) = elem!1),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1416, 1472, 733])).
% 1.64/1.89 tff(1474,plain,
% 1.64/1.89 (s(s(s(z))) = s(elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1473])).
% 1.64/1.89 tff(1475,plain,
% 1.64/1.89 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1474])).
% 1.64/1.89 tff(1476,plain,
% 1.64/1.89 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1475])).
% 1.64/1.89 tff(1477,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1476])).
% 1.64/1.89 tff(1478,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), z)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1469, 1477])).
% 1.64/1.89 tff(1479,plain,
% 1.64/1.89 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(1480,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 1.64/1.89 tff(1481,plain,
% 1.64/1.89 (s(s(elem!1)) = s(elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1480])).
% 1.64/1.89 tff(1482,plain,
% 1.64/1.89 (s(s(elem!1)) = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[1481, 1480])).
% 1.64/1.89 tff(1483,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1482])).
% 1.64/1.89 tff(1484,plain,
% 1.64/1.89 (s(s(s(elem!1))) = elem!1),
% 1.64/1.89 inference(transitivity,[status(thm)],[1483, 1480])).
% 1.64/1.89 tff(1485,plain,
% 1.64/1.89 ((s(s(s(elem!1))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1484])).
% 1.64/1.89 tff(1486,plain,
% 1.64/1.89 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.64/1.89 inference(transitivity,[status(thm)],[1485, 1479])).
% 1.64/1.89 tff(1487,plain,
% 1.64/1.89 ((s(s(z)) = elem!1) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.64/1.89 inference(symmetry,[status(thm)],[1486])).
% 1.64/1.89 tff(1488,plain,
% 1.64/1.89 (s(s(s(elem!1))) = s(s(z))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1418, 1487])).
% 1.64/1.89 tff(1489,assumption,(~(s(s(s(elem!1))) = s(s(z)))), introduced(assumption)).
% 1.64/1.89 tff(1490,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1489, 1488])).
% 1.64/1.89 tff(1491,plain,((~(s(s(z)) = elem!1)) | (s(s(s(elem!1))) = s(s(z))) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1492,plain,
% 1.64/1.89 ((~(s(s(z)) = elem!1)) | (~(s(elem!1) = elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1491, 1008])).
% 1.64/1.89 tff(1493,plain,
% 1.64/1.89 (~(s(elem!1) = elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1492, 1473])).
% 1.64/1.89 tff(1494,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1476, 1474])).
% 1.64/1.89 tff(1495,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1384, 1494])).
% 1.64/1.89 tff(1496,plain,
% 1.64/1.89 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(elem!1))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1474])).
% 1.64/1.89 tff(1497,plain,
% 1.64/1.89 ((~r(elem!1, s(s(s(z))))) <=> (~r(elem!1, s(elem!1)))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1496])).
% 1.64/1.89 tff(1498,plain,
% 1.64/1.89 (~r(elem!1, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[936, 1497])).
% 1.64/1.89 tff(1499,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1476])).
% 1.64/1.89 tff(1500,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1473])).
% 1.64/1.89 tff(1501,plain,
% 1.64/1.89 (b(s(s(s(s(s(z))))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[207, 1500])).
% 1.64/1.89 tff(1502,plain,
% 1.64/1.89 (b(s(s(s(elem!1))), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1501, 1499])).
% 1.64/1.89 tff(1503,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1504,plain,
% 1.64/1.89 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.64/1.89 inference(commutativity,[status(thm)],[])).
% 1.64/1.89 tff(1505,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1506,plain,
% 1.64/1.89 (s(elem!1) = elem!1),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 1.64/1.89 tff(1507,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1503, 1506])).
% 1.64/1.89 tff(1508,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1509,plain,
% 1.64/1.89 (~(elem!1 = s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1508, 1503])).
% 1.64/1.89 tff(1510,assumption,(~r(elem!1, s(elem!1))), introduced(assumption)).
% 1.64/1.89 tff(1511,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1512,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1513,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 1.64/1.89 tff(1514,plain,
% 1.64/1.89 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1513, 25, 1510])).
% 1.64/1.89 tff(1515,plain,
% 1.64/1.89 (b(elem!1, s(elem!1))),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1514, 1509])).
% 1.64/1.89 tff(1516,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1517,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1518,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 1.64/1.89 tff(1519,plain,
% 1.64/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1520,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.64/1.89 inference(quant_inst,[status(thm)],[])).
% 1.64/1.89 tff(1521,plain,
% 1.64/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.64/1.89 inference(modus_ponens,[status(thm)],[1520, 1519])).
% 1.64/1.89 tff(1522,plain,
% 1.64/1.89 ($false),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1521, 25, 1517, 1518, 1503])).
% 1.64/1.89 tff(1523,plain,(b(s(elem!1), elem!1) | r(s(elem!1), elem!1) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.64/1.89 tff(1524,plain,
% 1.64/1.89 (b(s(elem!1), elem!1)),
% 1.64/1.89 inference(unit_resolution,[status(thm)],[1523, 1503, 1517])).
% 1.64/1.89 tff(1525,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.64/1.89 tff(1526,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), elem!1)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1527,plain,
% 1.64/1.89 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(elem!1, s(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)))),
% 1.64/1.89 inference(rewrite,[status(thm)],[])).
% 1.64/1.89 tff(1528,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), elem!1))))),
% 1.64/1.89 inference(monotonicity,[status(thm)],[1527])).
% 1.64/1.89 tff(1529,plain,
% 1.64/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1), elem!1)))),
% 1.64/1.89 inference(transitivity,[status(thm)],[1528, 1526])).
% 1.64/1.90 tff(1530,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 1.64/1.90 inference(quant_inst,[status(thm)],[])).
% 1.64/1.90 tff(1531,plain,
% 1.64/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1))),
% 1.64/1.90 inference(modus_ponens,[status(thm)],[1530, 1529])).
% 1.64/1.90 tff(1532,plain,
% 1.64/1.90 ($false),
% 1.64/1.90 inference(unit_resolution,[status(thm)],[1531, 171, 1525, 1524, 1516, 1515])).
% 1.64/1.90 tff(1533,plain,((s(elem!1) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | r(elem!1, s(elem!1)) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1534,plain,
% 1.74/1.90 (r(s(elem!1), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1533, 1502, 1498, 1495, 1493])).
% 1.74/1.90 tff(1535,plain,
% 1.74/1.90 (~(s(elem!1) = s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[922, 1464])).
% 1.74/1.90 tff(1536,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 1.74/1.90 tff(1537,plain,
% 1.74/1.90 (s(elem!1) = s(z)),
% 1.74/1.90 inference(symmetry,[status(thm)],[1536])).
% 1.74/1.90 tff(1538,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[701, 1537])).
% 1.74/1.90 tff(1539,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1540,plain,
% 1.74/1.90 (~(s(z) = s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1539, 1535])).
% 1.74/1.90 tff(1541,plain,
% 1.74/1.90 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1476])).
% 1.74/1.90 tff(1542,plain,
% 1.74/1.90 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1473])).
% 1.74/1.90 tff(1543,plain,
% 1.74/1.90 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[160, 1542])).
% 1.74/1.90 tff(1544,plain,
% 1.74/1.90 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1543, 1541])).
% 1.74/1.90 tff(1545,assumption,(s(s(z)) = s(elem!1)), introduced(assumption)).
% 1.74/1.90 tff(1546,plain,
% 1.74/1.90 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1545])).
% 1.74/1.90 tff(1547,plain,
% 1.74/1.90 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1546])).
% 1.74/1.90 tff(1548,plain,
% 1.74/1.90 (elem!1 = inj_0(s(elem!1))),
% 1.74/1.90 inference(symmetry,[status(thm)],[916])).
% 1.74/1.90 tff(1549,plain,
% 1.74/1.90 (elem!1 = s(z)),
% 1.74/1.90 inference(transitivity,[status(thm)],[1548, 1547, 70])).
% 1.74/1.90 tff(1550,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1437, 1549])).
% 1.74/1.90 tff(1551,plain,((~(s(s(z)) = s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1552,plain,
% 1.74/1.90 (~(s(s(z)) = s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1551, 1434])).
% 1.74/1.90 tff(1553,plain,
% 1.74/1.90 (~(elem!1 = z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[697, 1464])).
% 1.74/1.90 tff(1554,assumption,(r(elem!1, z)), introduced(assumption)).
% 1.74/1.90 tff(1555,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1556,plain,
% 1.74/1.90 (((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1557,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1556])).
% 1.74/1.90 tff(1558,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1557, 1555])).
% 1.74/1.90 tff(1559,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1560,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 1.74/1.90 tff(1561,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1560, 106, 638, 1554, 96, 1446])).
% 1.74/1.90 tff(1562,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1563,plain,
% 1.74/1.90 (~r(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1562, 1465, 94, 1446])).
% 1.74/1.90 tff(1564,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1565,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1566,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1565, 1564])).
% 1.74/1.90 tff(1567,plain,
% 1.74/1.90 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1566, 25])).
% 1.74/1.90 tff(1568,plain,
% 1.74/1.90 (b(elem!1, z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1567, 1563, 1553])).
% 1.74/1.90 tff(1569,plain,
% 1.74/1.90 (b(elem!1, s(z))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[687, 676, 1434])).
% 1.74/1.90 tff(1570,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 1.74/1.90 tff(1571,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.74/1.90 tff(1572,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1573,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1574,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1573, 1572])).
% 1.74/1.90 tff(1575,plain,
% 1.74/1.90 (~r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1574, 106, 1571, 96, 95])).
% 1.74/1.90 tff(1576,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1577,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1578,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 1.74/1.90 tff(1579,plain,
% 1.74/1.90 (b(s(s(s(elem!1))), z)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1578, 25, 724, 1575])).
% 1.74/1.90 tff(1580,plain,
% 1.74/1.90 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(1581,plain,
% 1.74/1.90 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1580])).
% 1.74/1.90 tff(1582,plain,
% 1.74/1.90 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1581])).
% 1.74/1.90 tff(1583,plain,
% 1.74/1.90 (~(z = s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[724, 1582])).
% 1.74/1.90 tff(1584,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1585,plain,
% 1.74/1.90 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1586,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1585])).
% 1.74/1.90 tff(1587,plain,
% 1.74/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1586, 1584])).
% 1.74/1.90 tff(1588,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1589,plain,
% 1.74/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1588, 1587])).
% 1.74/1.90 tff(1590,plain,
% 1.74/1.90 (~r(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1589, 106, 1571, 96, 95])).
% 1.74/1.90 tff(1591,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1592,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1593,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1592, 1591])).
% 1.74/1.90 tff(1594,plain,
% 1.74/1.90 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1593, 25, 1590])).
% 1.74/1.90 tff(1595,plain,
% 1.74/1.90 (b(z, s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1594, 1583])).
% 1.74/1.90 tff(1596,assumption,(b(elem!1, z)), introduced(assumption)).
% 1.74/1.90 tff(1597,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1598,plain,
% 1.74/1.90 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1599,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1598])).
% 1.74/1.90 tff(1600,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1599, 1597])).
% 1.74/1.90 tff(1601,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1602,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1601, 1600])).
% 1.74/1.90 tff(1603,plain,
% 1.74/1.90 (~b(s(s(z)), elem!1)),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1602, 171, 1596, 1, 1595, 1579])).
% 1.74/1.90 tff(1604,plain,
% 1.74/1.90 (s(s(z)) = elem!1),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1416, 1603, 1570])).
% 1.74/1.90 tff(1605,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.74/1.90 tff(1606,plain,
% 1.74/1.90 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1605])).
% 1.74/1.90 tff(1607,plain,
% 1.74/1.90 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1606])).
% 1.74/1.90 tff(1608,plain,
% 1.74/1.90 (s(s(z)) = s(s(elem!1))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1418, 1548, 1607, 812])).
% 1.74/1.90 tff(1609,plain,
% 1.74/1.90 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1608])).
% 1.74/1.90 tff(1610,plain,
% 1.74/1.90 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1609])).
% 1.74/1.90 tff(1611,plain,
% 1.74/1.90 (s(elem!1) = s(z)),
% 1.74/1.90 inference(transitivity,[status(thm)],[1003, 1610, 70])).
% 1.74/1.90 tff(1612,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[701, 1611])).
% 1.74/1.90 tff(1613,plain,((~(s(s(z)) = elem!1)) | (s(elem!1) = s(z)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1614,plain,
% 1.74/1.90 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1613, 1604, 701])).
% 1.74/1.90 tff(1615,plain,
% 1.74/1.90 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(1616,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.90 tff(1617,plain,
% 1.74/1.90 (s(s(s(elem!1))) = s(elem!1)),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1616, 1615])).
% 1.74/1.90 tff(1618,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.74/1.90 tff(1619,plain,
% 1.74/1.90 ($false),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1618, 1617])).
% 1.74/1.90 tff(1620,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.90 tff(1621,plain,
% 1.74/1.90 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1620, 1614])).
% 1.74/1.90 tff(1622,plain,
% 1.74/1.90 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1604])).
% 1.74/1.90 tff(1623,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.74/1.90 inference(commutativity,[status(thm)],[])).
% 1.74/1.90 tff(1624,plain,
% 1.74/1.90 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.74/1.90 inference(symmetry,[status(thm)],[1623])).
% 1.74/1.90 tff(1625,plain,
% 1.74/1.90 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(elem!1)))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1624])).
% 1.74/1.90 tff(1626,plain,
% 1.74/1.90 (~(s(s(z)) = s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1008, 1625])).
% 1.74/1.90 tff(1627,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1628,plain,
% 1.74/1.90 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1629,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.74/1.90 inference(monotonicity,[status(thm)],[1628])).
% 1.74/1.90 tff(1630,plain,
% 1.74/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.90 inference(transitivity,[status(thm)],[1629, 1627])).
% 1.74/1.90 tff(1631,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1632,plain,
% 1.74/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.74/1.90 tff(1633,plain,
% 1.74/1.90 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.90 inference(unit_resolution,[status(thm)],[1632, 171, 1, 1595, 1579])).
% 1.74/1.90 tff(1634,plain,
% 1.74/1.90 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.90 inference(rewrite,[status(thm)],[])).
% 1.74/1.90 tff(1635,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.74/1.90 inference(quant_inst,[status(thm)],[])).
% 1.74/1.90 tff(1636,plain,
% 1.74/1.90 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.90 inference(modus_ponens,[status(thm)],[1635, 1634])).
% 1.74/1.90 tff(1637,plain,
% 1.74/1.90 ((s(s(z)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1636, 25, 1633])).
% 1.74/1.91 tff(1638,plain,
% 1.74/1.91 (r(s(s(z)), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1637, 1626])).
% 1.74/1.91 tff(1639,plain,
% 1.74/1.91 (r(elem!1, s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1638, 1622])).
% 1.74/1.91 tff(1640,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1604])).
% 1.74/1.91 tff(1641,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1642,plain,
% 1.74/1.91 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1643,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1642])).
% 1.74/1.91 tff(1644,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1643, 1641])).
% 1.74/1.91 tff(1645,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1646,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 1.74/1.91 tff(1647,plain,
% 1.74/1.91 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1646, 171, 1, 1595, 1579])).
% 1.74/1.91 tff(1648,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1013, 1647])).
% 1.74/1.91 tff(1649,plain,
% 1.74/1.91 (r(s(s(s(elem!1))), elem!1)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1648, 1640])).
% 1.74/1.91 tff(1650,plain,
% 1.74/1.91 (~(s(elem!1) = elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1492, 1604])).
% 1.74/1.91 tff(1651,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 1.74/1.91 tff(1652,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.91 tff(1653,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1654,plain,
% 1.74/1.91 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1655,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1654])).
% 1.74/1.91 tff(1656,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1655, 1653])).
% 1.74/1.91 tff(1657,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1658,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1657, 1656])).
% 1.74/1.91 tff(1659,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1658, 106, 638, 1652, 96, 1446])).
% 1.74/1.91 tff(1660,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1661,plain,
% 1.74/1.91 (~r(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1660, 1639, 638, 96])).
% 1.74/1.91 tff(1662,plain,
% 1.74/1.91 (b(s(z), elem!1)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1444, 1661, 1651])).
% 1.74/1.91 tff(1663,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.74/1.91 tff(1664,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1665,plain,
% 1.74/1.91 (((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1666,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1665])).
% 1.74/1.91 tff(1667,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1666, 1664])).
% 1.74/1.91 tff(1668,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1669,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1668, 1667])).
% 1.74/1.91 tff(1670,plain,
% 1.74/1.91 (~r(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1669, 106, 96, 1663, 95])).
% 1.74/1.91 tff(1671,plain,
% 1.74/1.91 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 1.74/1.91 inference(commutativity,[status(thm)],[])).
% 1.74/1.91 tff(1672,plain,
% 1.74/1.91 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 1.74/1.91 inference(symmetry,[status(thm)],[1671])).
% 1.74/1.91 tff(1673,plain,
% 1.74/1.91 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1672])).
% 1.74/1.91 tff(1674,plain,
% 1.74/1.91 (~(z = s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1006, 1673])).
% 1.74/1.91 tff(1675,plain,
% 1.74/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1676,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1677,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 1.74/1.91 tff(1678,plain,
% 1.74/1.91 ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1677, 25])).
% 1.74/1.91 tff(1679,plain,
% 1.74/1.91 (b(z, s(elem!1)) | r(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1678, 1674])).
% 1.74/1.91 tff(1680,plain,
% 1.74/1.91 (b(z, s(elem!1))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1679, 1670])).
% 1.74/1.91 tff(1681,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1682,plain,
% 1.74/1.91 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1683,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1682])).
% 1.74/1.91 tff(1684,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1683, 1681])).
% 1.74/1.91 tff(1685,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1686,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1685, 1684])).
% 1.74/1.91 tff(1687,plain,
% 1.74/1.91 (~r(s(elem!1), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1686, 106, 96, 1663, 95])).
% 1.74/1.91 tff(1688,plain,
% 1.74/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1689,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1690,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1689, 1688])).
% 1.74/1.91 tff(1691,plain,
% 1.74/1.91 (b(s(elem!1), z) | r(s(elem!1), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1690, 25, 1006])).
% 1.74/1.91 tff(1692,plain,
% 1.74/1.91 (b(s(elem!1), z)),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1691, 1687])).
% 1.74/1.91 tff(1693,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.91 tff(1694,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1695,plain,
% 1.74/1.91 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1696,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1695])).
% 1.74/1.91 tff(1697,plain,
% 1.74/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1696, 1694])).
% 1.74/1.91 tff(1698,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1699,plain,
% 1.74/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 1.74/1.91 tff(1700,plain,
% 1.74/1.91 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1699, 106, 1571, 1663, 95])).
% 1.74/1.91 tff(1701,plain,
% 1.74/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1702,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1703,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1702, 1701])).
% 1.74/1.91 tff(1704,plain,
% 1.74/1.91 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1703, 25, 1700, 1693])).
% 1.74/1.91 tff(1705,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1706,plain,
% 1.74/1.91 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1707,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 1.74/1.91 inference(monotonicity,[status(thm)],[1706])).
% 1.74/1.91 tff(1708,plain,
% 1.74/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 1.74/1.91 inference(transitivity,[status(thm)],[1707, 1705])).
% 1.74/1.91 tff(1709,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1710,plain,
% 1.74/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1709, 1708])).
% 1.74/1.91 tff(1711,plain,
% 1.74/1.91 ($false),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1710, 171, 1704, 1692, 1680, 1579])).
% 1.74/1.91 tff(1712,plain,((~r(s(elem!1), s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.91 tff(1713,plain,
% 1.74/1.91 (~r(s(elem!1), s(z))),
% 1.74/1.91 inference(unit_resolution,[status(thm)],[1712, 1621, 96, 95, 1571])).
% 1.74/1.91 tff(1714,plain,
% 1.74/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.74/1.91 inference(rewrite,[status(thm)],[])).
% 1.74/1.91 tff(1715,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.74/1.91 inference(quant_inst,[status(thm)],[])).
% 1.74/1.91 tff(1716,plain,
% 1.74/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.74/1.91 inference(modus_ponens,[status(thm)],[1715, 1714])).
% 1.74/1.91 tff(1717,plain,
% 1.74/1.91 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1716, 25])).
% 1.74/1.92 tff(1718,plain,
% 1.74/1.92 (b(s(elem!1), s(z))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1717, 1713, 701])).
% 1.74/1.92 tff(1719,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1720,plain,
% 1.74/1.92 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1721,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1720])).
% 1.74/1.92 tff(1722,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1721, 1719])).
% 1.74/1.92 tff(1723,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1724,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1723, 1722])).
% 1.74/1.92 tff(1725,plain,
% 1.74/1.92 (~b(s(elem!1), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1724, 171, 1596, 679, 1718, 1662])).
% 1.74/1.92 tff(1726,plain,
% 1.74/1.92 (r(s(elem!1), elem!1)),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1523, 1725, 1650])).
% 1.74/1.92 tff(1727,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1728,plain,
% 1.74/1.92 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1729,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1728])).
% 1.74/1.92 tff(1730,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1729, 1727])).
% 1.74/1.92 tff(1731,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1732,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 1.74/1.92 tff(1733,plain,
% 1.74/1.92 ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1732, 106])).
% 1.74/1.92 tff(1734,plain,
% 1.74/1.92 (~r(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1733, 1726, 1649, 1639])).
% 1.74/1.92 tff(1735,plain,
% 1.74/1.92 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1703, 25, 1734, 1621])).
% 1.74/1.92 tff(1736,plain,
% 1.74/1.92 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1604])).
% 1.74/1.92 tff(1737,plain,
% 1.74/1.92 (b(s(z), elem!1) <=> b(s(z), s(s(z)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[1736])).
% 1.74/1.92 tff(1738,plain,
% 1.74/1.92 (b(s(z), s(s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1662, 1737])).
% 1.74/1.92 tff(1739,assumption,(~(s(s(z)) = s(elem!1))), introduced(assumption)).
% 1.74/1.92 tff(1740,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 1.74/1.92 tff(1741,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1742,plain,
% 1.74/1.92 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1743,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1742])).
% 1.74/1.92 tff(1744,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1743, 1741])).
% 1.74/1.92 tff(1745,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1746,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1745, 1744])).
% 1.74/1.92 tff(1747,plain,
% 1.74/1.92 (~b(s(s(z)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1746, 171, 323, 259, 1740])).
% 1.74/1.92 tff(1748,plain,
% 1.74/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1749,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1750,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1749, 1748])).
% 1.74/1.92 tff(1751,plain,
% 1.74/1.92 (r(s(s(z)), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1750, 25, 1747, 1739])).
% 1.74/1.92 tff(1752,plain,
% 1.74/1.92 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.74/1.92 inference(commutativity,[status(thm)],[])).
% 1.74/1.92 tff(1753,plain,
% 1.74/1.92 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.74/1.92 inference(symmetry,[status(thm)],[1752])).
% 1.74/1.92 tff(1754,plain,
% 1.74/1.92 ((~(s(s(z)) = s(elem!1))) <=> (~(s(elem!1) = s(s(z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1753])).
% 1.74/1.92 tff(1755,plain,
% 1.74/1.92 (~(s(elem!1) = s(s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1739, 1754])).
% 1.74/1.92 tff(1756,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1757,plain,
% 1.74/1.92 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1758,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1757])).
% 1.74/1.92 tff(1759,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1758, 1756])).
% 1.74/1.92 tff(1760,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1761,plain,
% 1.74/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.74/1.92 tff(1762,plain,
% 1.74/1.92 ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1761, 171, 323, 1740, 1])).
% 1.74/1.92 tff(1763,plain,
% 1.74/1.92 (~b(s(elem!1), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1762, 259])).
% 1.74/1.92 tff(1764,plain,
% 1.74/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1765,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1766,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1765, 1764])).
% 1.74/1.92 tff(1767,plain,
% 1.74/1.92 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1766, 25, 1763])).
% 1.74/1.92 tff(1768,plain,
% 1.74/1.92 (r(s(elem!1), s(s(z)))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1767, 1755])).
% 1.74/1.92 tff(1769,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.92 tff(1770,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 1.74/1.92 tff(1771,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1772,plain,
% 1.74/1.92 (((~r(s(elem!1), s(s(z)))) | (~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(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1773,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1)))))),
% 1.74/1.92 inference(monotonicity,[status(thm)],[1772])).
% 1.74/1.92 tff(1774,plain,
% 1.74/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))))),
% 1.74/1.92 inference(transitivity,[status(thm)],[1773, 1771])).
% 1.74/1.92 tff(1775,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~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))))))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1776,plain,
% 1.74/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1)))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1775, 1774])).
% 1.74/1.92 tff(1777,plain,
% 1.74/1.92 ($false),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1776, 106, 1770, 1769, 1768, 1751])).
% 1.74/1.92 tff(1778,plain,((~b(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (s(s(z)) = s(elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.92 tff(1779,plain,
% 1.74/1.92 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1778, 1718, 1, 1739, 1638, 1738, 259])).
% 1.74/1.92 tff(1780,plain,
% 1.74/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1781,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 1.74/1.92 inference(quant_inst,[status(thm)],[])).
% 1.74/1.92 tff(1782,plain,
% 1.74/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.92 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 1.74/1.92 tff(1783,plain,
% 1.74/1.92 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1782, 25])).
% 1.74/1.92 tff(1784,plain,
% 1.74/1.92 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.92 inference(unit_resolution,[status(thm)],[1783, 1779, 1614])).
% 1.74/1.92 tff(1785,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1786,plain,
% 1.74/1.92 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.92 inference(rewrite,[status(thm)],[])).
% 1.74/1.92 tff(1787,plain,
% 1.74/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1786])).
% 1.74/1.93 tff(1788,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1787, 1785])).
% 1.74/1.93 tff(1789,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1790,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(s(s(elem!1)))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1789, 1788])).
% 1.74/1.93 tff(1791,plain,
% 1.74/1.93 ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1790, 171, 1784, 1718, 1595])).
% 1.74/1.93 tff(1792,plain,
% 1.74/1.93 (~b(z, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1791, 1735])).
% 1.74/1.93 tff(1793,plain,
% 1.74/1.93 (r(z, s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1679, 1792])).
% 1.74/1.93 tff(1794,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1795,plain,
% 1.74/1.93 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1796,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1795])).
% 1.74/1.93 tff(1797,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1796, 1794])).
% 1.74/1.93 tff(1798,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1799,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 1.74/1.93 tff(1800,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1799, 106, 638, 1639, 1726, 1793])).
% 1.74/1.93 tff(1801,plain,((~b(elem!1, z)) | (~r(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), z)) | (s(s(z)) = s(elem!1)) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(z) = elem!1) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1802,plain,
% 1.74/1.93 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1801, 1472, 94, 259, 1535, 95, 1569, 1467, 1568, 1465, 1440, 1552])).
% 1.74/1.93 tff(1803,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1804,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1805,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 1.74/1.93 tff(1806,plain,
% 1.74/1.93 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1805, 25])).
% 1.74/1.93 tff(1807,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1806, 818])).
% 1.74/1.93 tff(1808,plain,
% 1.74/1.93 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1807, 1802])).
% 1.74/1.93 tff(1809,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.74/1.93 tff(1810,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.74/1.93 tff(1811,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1812,plain,
% 1.74/1.93 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1813,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1812])).
% 1.74/1.93 tff(1814,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z)))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1813, 1811])).
% 1.74/1.93 tff(1815,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1816,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(z))))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 1.74/1.93 tff(1817,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1816, 106, 554, 1810, 96, 1663])).
% 1.74/1.93 tff(1818,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1819,plain,
% 1.74/1.93 (~r(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1818, 1810, 96, 554])).
% 1.74/1.93 tff(1820,plain,
% 1.74/1.93 (b(s(elem!1), s(z))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1717, 1819, 701])).
% 1.74/1.93 tff(1821,plain,
% 1.74/1.93 (~(s(z) = s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1539, 701])).
% 1.74/1.93 tff(1822,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.74/1.93 tff(1823,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1824,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1825,plain,
% 1.74/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1824, 1823])).
% 1.74/1.93 tff(1826,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1825, 106, 638, 1810, 95, 1822])).
% 1.74/1.93 tff(1827,plain,((~r(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1828,plain,
% 1.74/1.93 (~r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1827, 1810, 95, 638])).
% 1.74/1.93 tff(1829,plain,
% 1.74/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1830,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1831,plain,
% 1.74/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1830, 1829])).
% 1.74/1.93 tff(1832,plain,
% 1.74/1.93 ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1831, 25])).
% 1.74/1.93 tff(1833,plain,
% 1.74/1.93 (b(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1832, 1828, 1821])).
% 1.74/1.93 tff(1834,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.74/1.93 tff(1835,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1836,plain,
% 1.74/1.93 (((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, 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(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1837,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1836])).
% 1.74/1.93 tff(1838,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1837, 1835])).
% 1.74/1.93 tff(1839,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1840,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1839, 1838])).
% 1.74/1.93 tff(1841,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1840, 171, 1809, 679, 1740, 1834, 944])).
% 1.74/1.93 tff(1842,plain,((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1843,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1842, 1833, 1820, 679, 1809, 944])).
% 1.74/1.93 tff(1844,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1845,plain,
% 1.74/1.93 (~r(s(elem!1), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1844, 1569, 1808, 1544, 1535, 95, 1465, 94, 554])).
% 1.74/1.93 tff(1846,plain,
% 1.74/1.93 (b(s(elem!1), z)),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1691, 1845])).
% 1.74/1.93 tff(1847,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.74/1.93 tff(1848,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1849,plain,
% 1.74/1.93 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1850,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1849])).
% 1.74/1.93 tff(1851,plain,
% 1.74/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 1.74/1.93 inference(transitivity,[status(thm)],[1850, 1848])).
% 1.74/1.93 tff(1852,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/1.93 inference(quant_inst,[status(thm)],[])).
% 1.74/1.93 tff(1853,plain,
% 1.74/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))),
% 1.74/1.93 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 1.74/1.93 tff(1854,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1853, 171, 1596, 1809, 679, 1516, 1834, 1847])).
% 1.74/1.93 tff(1855,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1856,plain,
% 1.74/1.93 (~b(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1855, 1568, 1808, 1569, 1502, 1846])).
% 1.74/1.93 tff(1857,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 1.74/1.93 tff(1858,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 1.74/1.93 tff(1859,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 1.74/1.93 tff(1860,plain,
% 1.74/1.93 ($false),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1831, 25, 1859, 1858, 1857])).
% 1.74/1.93 tff(1861,plain,(b(s(z), s(elem!1)) | r(s(z), s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.93 tff(1862,plain,
% 1.74/1.93 (r(s(z), s(elem!1))),
% 1.74/1.93 inference(unit_resolution,[status(thm)],[1861, 1856, 1540])).
% 1.74/1.93 tff(1863,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1864,plain,
% 1.74/1.93 (((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))) <=> ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.93 inference(rewrite,[status(thm)],[])).
% 1.74/1.93 tff(1865,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))))),
% 1.74/1.93 inference(monotonicity,[status(thm)],[1864])).
% 1.74/1.93 tff(1866,plain,
% 1.74/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1865, 1863])).
% 1.74/1.94 tff(1867,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1868,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1867, 1866])).
% 1.74/1.94 tff(1869,plain,
% 1.74/1.94 ((~r(z, s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(z), s(elem!1)))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1868, 106])).
% 1.74/1.94 tff(1870,plain,
% 1.74/1.94 (~r(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1869, 1862, 95, 1534])).
% 1.74/1.94 tff(1871,plain,
% 1.74/1.94 (b(z, s(elem!1))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1679, 1870])).
% 1.74/1.94 tff(1872,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1873,plain,
% 1.74/1.94 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1874,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1873])).
% 1.74/1.94 tff(1875,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1874, 1872])).
% 1.74/1.94 tff(1876,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1877,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1876, 1875])).
% 1.74/1.94 tff(1878,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1877, 171, 1568, 1502, 1846, 1871, 1478])).
% 1.74/1.94 tff(1879,plain,(r(elem!1, s(z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | r(elem!1, 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(z))) | b(s(s(z)), elem!1) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | b(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1880,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1879, 1463, 1462, 1386, 1384, 95, 207, 160, 259, 733, 126, 1383, 258, 84])).
% 1.74/1.94 tff(1881,plain,(b(s(s(z)), elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | b(z, elem!1) | b(z, s(z)) | b(s(z), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1882,plain,
% 1.74/1.94 (b(s(s(z)), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1881, 1369, 95, 614, 1356, 259, 126, 258, 84, 545])).
% 1.74/1.94 tff(1883,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1884,plain,
% 1.74/1.94 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1885,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1884])).
% 1.74/1.94 tff(1886,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1885, 1883])).
% 1.74/1.94 tff(1887,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1888,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1887, 1886])).
% 1.74/1.94 tff(1889,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1888, 171, 666, 840, 160, 207])).
% 1.74/1.94 tff(1890,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1891,plain,
% 1.74/1.94 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1890, 1882, 614, 1356])).
% 1.74/1.94 tff(1892,plain,
% 1.74/1.94 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[672])).
% 1.74/1.94 tff(1893,plain,
% 1.74/1.94 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1892, 759])).
% 1.74/1.94 tff(1894,plain,
% 1.74/1.94 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1893])).
% 1.74/1.94 tff(1895,plain,
% 1.74/1.94 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[140, 1894])).
% 1.74/1.94 tff(1896,plain,
% 1.74/1.94 (r(elem!1, s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[691, 672, 84])).
% 1.74/1.94 tff(1897,plain,
% 1.74/1.94 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.94 inference(transitivity,[status(thm)],[1893, 760])).
% 1.74/1.94 tff(1898,plain,
% 1.74/1.94 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1897])).
% 1.74/1.94 tff(1899,plain,
% 1.74/1.94 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[140, 1898])).
% 1.74/1.94 tff(1900,assumption,(~(s(s(s(s(s(z))))) = elem!1)), introduced(assumption)).
% 1.74/1.94 tff(1901,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1902,plain,
% 1.74/1.94 (((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1903,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1902])).
% 1.74/1.94 tff(1904,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1903, 1901])).
% 1.74/1.94 tff(1905,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1906,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1905, 1904])).
% 1.74/1.94 tff(1907,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1906, 106, 554, 730, 502])).
% 1.74/1.94 tff(1908,assumption,(~(elem!1 = s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/1.94 tff(1909,plain,
% 1.74/1.94 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[782, 778, 1908])).
% 1.74/1.94 tff(1910,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1911,plain,
% 1.74/1.94 (((~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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1912,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1911])).
% 1.74/1.94 tff(1913,plain,
% 1.74/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1912, 1910])).
% 1.74/1.94 tff(1914,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1915,plain,
% 1.74/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1914, 1913])).
% 1.74/1.94 tff(1916,plain,
% 1.74/1.94 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1915, 171, 666, 83, 1909, 160])).
% 1.74/1.94 tff(1917,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[853, 1916, 1907, 1900])).
% 1.74/1.94 tff(1918,plain,((~r(s(s(s(s(s(z))))), s(z))) | (s(s(s(s(s(z))))) = elem!1) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1919,plain,
% 1.74/1.94 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1918, 1899, 551, 83, 666, 160, 1896, 1895, 95])).
% 1.74/1.94 tff(1920,plain,
% 1.74/1.94 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[479, 1919])).
% 1.74/1.94 tff(1921,plain,
% 1.74/1.94 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.74/1.94 inference(monotonicity,[status(thm)],[672])).
% 1.74/1.94 tff(1922,plain,
% 1.74/1.94 (r(s(z), elem!1) <=> r(s(z), z)),
% 1.74/1.94 inference(symmetry,[status(thm)],[1921])).
% 1.74/1.94 tff(1923,plain,
% 1.74/1.94 ((~r(s(z), elem!1)) <=> (~r(s(z), z))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1922])).
% 1.74/1.94 tff(1924,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 1.74/1.94 tff(1925,plain,
% 1.74/1.94 (~r(s(z), z)),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1924, 1923])).
% 1.74/1.94 tff(1926,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[95, 1925])).
% 1.74/1.94 tff(1927,plain,((~(z = elem!1)) | (~r(s(z), z)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1928,plain,
% 1.74/1.94 (r(s(z), elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1927, 672, 95])).
% 1.74/1.94 tff(1929,plain,
% 1.74/1.94 (~(s(s(s(z))) = elem!1)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[788, 672])).
% 1.74/1.94 tff(1930,plain,
% 1.74/1.94 (s(elem!1) = s(z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[703, 672])).
% 1.74/1.94 tff(1931,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1932,plain,
% 1.74/1.94 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1933,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1932])).
% 1.74/1.94 tff(1934,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1933, 1931])).
% 1.74/1.94 tff(1935,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1936,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1935, 1934])).
% 1.74/1.94 tff(1937,plain,
% 1.74/1.94 ($false),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1936, 106, 554, 730, 1426, 747])).
% 1.74/1.94 tff(1938,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.94 tff(1939,plain,
% 1.74/1.94 (~r(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1938, 1896, 554, 1426])).
% 1.74/1.94 tff(1940,plain,
% 1.74/1.94 (b(s(s(s(z))), s(z))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1173, 1939])).
% 1.74/1.94 tff(1941,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1942,plain,
% 1.74/1.94 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1943,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1942])).
% 1.74/1.94 tff(1944,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1943, 1941])).
% 1.74/1.94 tff(1945,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1946,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1945, 1944])).
% 1.74/1.94 tff(1947,plain,
% 1.74/1.94 (~r(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1946, 106, 554, 96, 263])).
% 1.74/1.94 tff(1948,plain,
% 1.74/1.94 (b(s(s(s(s(z)))), z)),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[274, 1947])).
% 1.74/1.94 tff(1949,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1950,plain,
% 1.74/1.94 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.94 inference(rewrite,[status(thm)],[])).
% 1.74/1.94 tff(1951,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.74/1.94 inference(monotonicity,[status(thm)],[1950])).
% 1.74/1.94 tff(1952,plain,
% 1.74/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.94 inference(transitivity,[status(thm)],[1951, 1949])).
% 1.74/1.94 tff(1953,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.74/1.94 inference(quant_inst,[status(thm)],[])).
% 1.74/1.94 tff(1954,plain,
% 1.74/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.74/1.94 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.74/1.94 tff(1955,plain,
% 1.74/1.94 (~r(z, s(s(s(s(z)))))),
% 1.74/1.94 inference(unit_resolution,[status(thm)],[1954, 106, 554, 96, 263])).
% 1.74/1.94 tff(1956,plain,
% 1.74/1.95 (b(z, s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[293, 1955])).
% 1.74/1.95 tff(1957,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[310, 171, 83, 304, 1956, 1948])).
% 1.74/1.95 tff(1958,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1959,plain,
% 1.74/1.95 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1958, 554, 83, 94, 126, 260])).
% 1.74/1.95 tff(1960,plain,
% 1.74/1.95 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[321, 1959, 255])).
% 1.74/1.95 tff(1961,plain,
% 1.74/1.95 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[672])).
% 1.74/1.95 tff(1962,plain,
% 1.74/1.95 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[1961])).
% 1.74/1.95 tff(1963,plain,
% 1.74/1.95 (r(z, s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1426, 1962])).
% 1.74/1.95 tff(1964,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[712])).
% 1.74/1.95 tff(1965,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.95 inference(symmetry,[status(thm)],[1964])).
% 1.74/1.95 tff(1966,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1918, 160, 666, 83, 1900, 554, 730, 1908, 95])).
% 1.74/1.95 tff(1967,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[479, 1966])).
% 1.74/1.95 tff(1968,plain,
% 1.74/1.95 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[445, 1967, 357, 259])).
% 1.74/1.95 tff(1969,plain,
% 1.74/1.95 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[454, 1968, 254])).
% 1.74/1.95 tff(1970,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1365, 1969, 126, 260])).
% 1.74/1.95 tff(1971,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1368, 1970])).
% 1.74/1.95 tff(1972,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1971, 1965])).
% 1.74/1.95 tff(1973,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[463, 1969, 126, 260])).
% 1.74/1.95 tff(1974,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[225, 1973])).
% 1.74/1.95 tff(1975,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(1976,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(1977,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1978,plain,
% 1.74/1.95 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1979,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[1978])).
% 1.74/1.95 tff(1980,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[1979, 1977])).
% 1.74/1.95 tff(1981,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1982,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 1.74/1.95 tff(1983,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1982, 171, 259, 1188, 1976, 4, 207])).
% 1.74/1.95 tff(1984,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1985,plain,
% 1.74/1.95 (~b(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1984, 1974, 259, 1188, 1967])).
% 1.74/1.95 tff(1986,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.74/1.95 tff(1987,plain,
% 1.74/1.95 (s(s(s(z))) = s(z)),
% 1.74/1.95 inference(symmetry,[status(thm)],[1986])).
% 1.74/1.95 tff(1988,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[344, 1987])).
% 1.74/1.95 tff(1989,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1990,assumption,(~r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(1991,assumption,(~b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(1992,plain,
% 1.74/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(1993,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(1994,plain,
% 1.74/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 1.74/1.95 tff(1995,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1994, 25, 1991, 1990, 1989])).
% 1.74/1.95 tff(1996,plain,(r(s(z), s(s(s(z)))) | b(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(1997,plain,
% 1.74/1.95 (r(s(z), s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1996, 1985])).
% 1.74/1.95 tff(1998,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(1999,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2000,plain,
% 1.74/1.95 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2001,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2000])).
% 1.74/1.95 tff(2002,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2001, 1999])).
% 1.74/1.95 tff(2003,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2004,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2003, 2002])).
% 1.74/1.95 tff(2005,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2004, 106, 96, 1199, 1998, 1975])).
% 1.74/1.95 tff(2006,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2007,plain,
% 1.74/1.95 (~r(s(s(s(z))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2006, 1997, 96, 1975])).
% 1.74/1.95 tff(2008,plain,
% 1.74/1.95 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[995, 2007, 710])).
% 1.74/1.95 tff(2009,plain,
% 1.74/1.95 (b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[1013, 2008])).
% 1.74/1.95 tff(2010,assumption,(b(s(s(s(s(s(z))))), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.95 tff(2011,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2012,plain,
% 1.74/1.95 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(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(elem!1))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2013,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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(elem!1)))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2012])).
% 1.74/1.95 tff(2014,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(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(elem!1))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2013, 2011])).
% 1.74/1.95 tff(2015,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2016,plain,
% 1.74/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2015, 2014])).
% 1.74/1.95 tff(2017,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2016, 171, 1016, 160, 207, 2010])).
% 1.74/1.95 tff(2018,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(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(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2019,plain,
% 1.74/1.95 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2018, 2009, 160, 1974])).
% 1.74/1.95 tff(2020,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2019, 1972])).
% 1.74/1.95 tff(2021,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = elem!1) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2022,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2021, 1963, 1899, 94, 160, 259, 1930, 126, 260, 1960, 666, 83, 1940, 554, 1896, 1895, 95])).
% 1.74/1.95 tff(2023,plain,((~(z = elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2024,plain,
% 1.74/1.95 (~r(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2023, 672, 259, 126, 260, 551, 83, 160, 95, 666, 84])).
% 1.74/1.95 tff(2025,plain,
% 1.74/1.95 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[942, 1930, 2024])).
% 1.74/1.95 tff(2026,plain,
% 1.74/1.95 (b(elem!1, s(s(s(z))))),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[948, 2025, 1930])).
% 1.74/1.95 tff(2027,assumption,(r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 1.74/1.95 tff(2028,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2029,plain,
% 1.74/1.95 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2030,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2029])).
% 1.74/1.95 tff(2031,plain,
% 1.74/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(transitivity,[status(thm)],[2030, 2028])).
% 1.74/1.95 tff(2032,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.95 inference(quant_inst,[status(thm)],[])).
% 1.74/1.95 tff(2033,plain,
% 1.74/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.74/1.95 inference(modus_ponens,[status(thm)],[2032, 2031])).
% 1.74/1.95 tff(2034,plain,
% 1.74/1.95 ($false),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2033, 106, 730, 1446, 2027, 126])).
% 1.74/1.95 tff(2035,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.95 tff(2036,plain,
% 1.74/1.95 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[2035, 1896, 1928, 126])).
% 1.74/1.95 tff(2037,plain,
% 1.74/1.95 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/1.95 inference(unit_resolution,[status(thm)],[853, 2036, 1899])).
% 1.74/1.95 tff(2038,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.74/1.95 tff(2039,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2040,plain,
% 1.74/1.95 (((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.95 inference(rewrite,[status(thm)],[])).
% 1.74/1.95 tff(2041,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/1.95 inference(monotonicity,[status(thm)],[2040])).
% 1.74/1.95 tff(2042,plain,
% 1.74/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2041, 2039])).
% 1.74/1.96 tff(2043,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2044,plain,
% 1.74/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 1.74/1.96 tff(2045,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2044, 171, 839, 1384, 837, 2038])).
% 1.74/1.96 tff(2046,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2047,plain,
% 1.74/1.96 (~b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2046, 2037, 1369, 2026])).
% 1.74/1.96 tff(2048,plain,
% 1.74/1.96 (r(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[804, 2047, 1929])).
% 1.74/1.96 tff(2049,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.74/1.96 tff(2050,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2051,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2052,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2051, 2050])).
% 1.74/1.96 tff(2053,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2052, 106, 730, 1446, 2049, 747])).
% 1.74/1.96 tff(2054,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2055,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2054, 2048, 1928, 1896])).
% 1.74/1.96 tff(2056,plain,
% 1.74/1.96 (b(s(s(s(z))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1173, 2055])).
% 1.74/1.96 tff(2057,plain,
% 1.74/1.96 (~b(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1984, 2056, 259, 1920, 614])).
% 1.74/1.96 tff(2058,plain,
% 1.74/1.96 (r(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1996, 2057])).
% 1.74/1.96 tff(2059,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2060,plain,
% 1.74/1.96 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2061,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2060])).
% 1.74/1.96 tff(2062,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2061, 2059])).
% 1.74/1.96 tff(2063,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2064,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2063, 2062])).
% 1.74/1.96 tff(2065,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2064, 106, 1896, 1928, 2048, 2058])).
% 1.74/1.96 tff(2066,plain,((~(z = elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2067,plain,
% 1.74/1.96 (~(z = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2066, 1882, 126, 83, 259, 1356, 95, 260, 84])).
% 1.74/1.96 tff(2068,plain,
% 1.74/1.96 (r(z, elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[651, 2067, 258])).
% 1.74/1.96 tff(2069,plain,
% 1.74/1.96 (~r(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1376, 2068, 94, 95])).
% 1.74/1.96 tff(2070,plain,
% 1.74/1.96 (~(s(elem!1) = s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[922, 2067])).
% 1.74/1.96 tff(2071,plain,
% 1.74/1.96 (~r(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[646, 2068, 551, 95])).
% 1.74/1.96 tff(2072,plain,
% 1.74/1.96 (b(s(s(z)), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[157, 2071])).
% 1.74/1.96 tff(2073,plain,
% 1.74/1.96 (~r(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1398, 2068, 95, 126])).
% 1.74/1.96 tff(2074,plain,
% 1.74/1.96 (b(s(s(s(s(s(z))))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[145, 2073])).
% 1.74/1.96 tff(2075,plain,
% 1.74/1.96 (~b(z, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[215, 2074, 614, 2072])).
% 1.74/1.96 tff(2076,plain,
% 1.74/1.96 (r(z, s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[124, 2075])).
% 1.74/1.96 tff(2077,plain,
% 1.74/1.96 (~r(s(s(z)), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1411, 2076, 94, 551])).
% 1.74/1.96 tff(2078,plain,
% 1.74/1.96 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 1.74/1.96 inference(commutativity,[status(thm)],[])).
% 1.74/1.96 tff(2079,plain,
% 1.74/1.96 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2078])).
% 1.74/1.96 tff(2080,plain,
% 1.74/1.96 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2079])).
% 1.74/1.96 tff(2081,plain,
% 1.74/1.96 (~(z = s(s(elem!1)))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[816, 2080])).
% 1.74/1.96 tff(2082,plain,
% 1.74/1.96 (s(s(z)) = s(elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1435])).
% 1.74/1.96 tff(2083,plain,
% 1.74/1.96 (s(s(s(z))) = s(s(elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2082])).
% 1.74/1.96 tff(2084,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2083])).
% 1.74/1.96 tff(2085,plain,
% 1.74/1.96 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2084])).
% 1.74/1.96 tff(2086,plain,
% 1.74/1.96 (b(s(s(s(z))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[2085])).
% 1.74/1.96 tff(2087,plain,
% 1.74/1.96 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(elem!1)), elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2086])).
% 1.74/1.96 tff(2088,plain,
% 1.74/1.96 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1435])).
% 1.74/1.96 tff(2089,plain,
% 1.74/1.96 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[2088])).
% 1.74/1.96 tff(2090,plain,
% 1.74/1.96 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2089])).
% 1.74/1.96 tff(2091,plain,
% 1.74/1.96 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 1.74/1.96 inference(bind,[status(th)],[])).
% 1.74/1.96 tff(2092,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(quant_intro,[status(thm)],[2091])).
% 1.74/1.96 tff(2093,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2094,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 1.74/1.96 tff(2095,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2094, 2093])).
% 1.74/1.96 tff(2096,plain,(
% 1.74/1.96 ![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(skolemize,[status(sab)],[2095])).
% 1.74/1.96 tff(2097,plain,
% 1.74/1.96 (![X: $i] : (~b(X, X))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2096, 2092])).
% 1.74/1.96 tff(2098,plain,
% 1.74/1.96 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2099,plain,
% 1.74/1.96 (~b(elem!1, elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2098, 2097])).
% 1.74/1.96 tff(2100,plain,
% 1.74/1.96 (~b(s(z), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2099, 2090])).
% 1.74/1.96 tff(2101,plain,
% 1.74/1.96 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.96 inference(commutativity,[status(thm)],[])).
% 1.74/1.96 tff(2102,plain,
% 1.74/1.96 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2101])).
% 1.74/1.96 tff(2103,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(z))) <=> (s(s(s(z))) = elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1418])).
% 1.74/1.96 tff(2104,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(z))) <=> (elem!1 = s(s(s(z))))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2103, 2102])).
% 1.74/1.96 tff(2105,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(s(z)))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2104])).
% 1.74/1.96 tff(2106,plain,
% 1.74/1.96 (~(elem!1 = s(s(s(z))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[80, 2105])).
% 1.74/1.96 tff(2107,plain,
% 1.74/1.96 (b(s(s(z)), elem!1) <=> b(elem!1, elem!1)),
% 1.74/1.96 inference(monotonicity,[status(thm)],[1418])).
% 1.74/1.96 tff(2108,plain,
% 1.74/1.96 (b(elem!1, elem!1) <=> b(s(s(z)), elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[2107])).
% 1.74/1.96 tff(2109,plain,
% 1.74/1.96 ((~b(elem!1, elem!1)) <=> (~b(s(s(z)), elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2108])).
% 1.74/1.96 tff(2110,plain,
% 1.74/1.96 (~b(s(s(z)), elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2099, 2109])).
% 1.74/1.96 tff(2111,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1461, 2110, 95, 84, 258, 259, 1427])).
% 1.74/1.96 tff(2112,plain,
% 1.74/1.96 ((elem!1 = s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[939, 25, 946])).
% 1.74/1.96 tff(2113,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2112, 2111, 2106])).
% 1.74/1.96 tff(2114,plain,((~(s(s(z)) = elem!1)) | b(elem!1, s(s(s(z)))) | (~r(s(z), z)) | b(z, s(z)) | b(z, elem!1) | (~b(s(s(z)), s(z))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2115,plain,
% 1.74/1.96 (~(s(s(z)) = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2114, 1427, 95, 84, 258, 259, 946])).
% 1.74/1.96 tff(2116,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 1.74/1.96 tff(2117,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[374, 368, 355])).
% 1.74/1.96 tff(2118,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.74/1.96 tff(2119,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2120,plain,
% 1.74/1.96 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2121,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2120])).
% 1.74/1.96 tff(2122,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2121, 2119])).
% 1.74/1.96 tff(2123,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2124,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2123, 2122])).
% 1.74/1.96 tff(2125,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2124, 106, 95, 600, 263, 2118])).
% 1.74/1.96 tff(2126,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2127,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2126, 2118, 95, 600])).
% 1.74/1.96 tff(2128,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[321, 2127, 255])).
% 1.74/1.96 tff(2129,plain,
% 1.74/1.96 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[566, 2128, 259, 356])).
% 1.74/1.96 tff(2130,plain,
% 1.74/1.96 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[454, 2129, 254])).
% 1.74/1.96 tff(2131,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2132,plain,
% 1.74/1.96 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2133,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2132])).
% 1.74/1.96 tff(2134,plain,
% 1.74/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2133, 2131])).
% 1.74/1.96 tff(2135,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2136,plain,
% 1.74/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2135, 2134])).
% 1.74/1.96 tff(2137,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2136, 106, 96, 95, 2130, 2118])).
% 1.74/1.96 tff(2138,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2139,plain,
% 1.74/1.96 (~r(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2138, 600, 95, 259, 2117, 94])).
% 1.74/1.96 tff(2140,plain,
% 1.74/1.96 (b(s(s(s(s(z)))), z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[274, 2139])).
% 1.74/1.96 tff(2141,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.74/1.96 tff(2142,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.74/1.96 tff(2143,plain,
% 1.74/1.96 (b(s(z), elem!1) <=> b(s(z), s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2142])).
% 1.74/1.96 tff(2144,plain,
% 1.74/1.96 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2143])).
% 1.74/1.96 tff(2145,plain,
% 1.74/1.96 (~b(s(z), s(s(s(z))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[1427, 2144])).
% 1.74/1.96 tff(2146,plain,
% 1.74/1.96 (r(s(z), s(s(s(z))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1994, 25, 2145, 1989])).
% 1.74/1.96 tff(2147,plain,
% 1.74/1.96 (s(s(s(z))) = elem!1),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2142, 2101])).
% 1.74/1.96 tff(2148,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[797, 2147])).
% 1.74/1.96 tff(2149,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2150,plain,
% 1.74/1.96 (s(s(s(z))) = elem!1),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2149, 2142])).
% 1.74/1.96 tff(2151,plain,
% 1.74/1.96 (~(z = elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[788, 2150])).
% 1.74/1.96 tff(2152,plain,
% 1.74/1.96 (r(z, elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[651, 2151, 258])).
% 1.74/1.96 tff(2153,plain,
% 1.74/1.96 (~(elem!1 = z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[697, 2151])).
% 1.74/1.96 tff(2154,plain,
% 1.74/1.96 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 1.74/1.96 inference(symmetry,[status(thm)],[671])).
% 1.74/1.96 tff(2155,plain,
% 1.74/1.96 ((elem!1 = s(z)) <=> (s(s(s(z))) = s(z))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2142])).
% 1.74/1.96 tff(2156,plain,
% 1.74/1.96 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(z))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2155])).
% 1.74/1.96 tff(2157,plain,
% 1.74/1.96 ((s(s(s(z))) = s(z)) <=> (s(z) = elem!1)),
% 1.74/1.96 inference(transitivity,[status(thm)],[2156, 2154])).
% 1.74/1.96 tff(2158,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = elem!1))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2157])).
% 1.74/1.96 tff(2159,plain,
% 1.74/1.96 (~(s(z) = elem!1)),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[344, 2158])).
% 1.74/1.96 tff(2160,plain,
% 1.74/1.96 (r(s(z), elem!1)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1444, 2159, 1427])).
% 1.74/1.96 tff(2161,plain,
% 1.74/1.96 (~r(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1562, 2160, 96, 2152])).
% 1.74/1.96 tff(2162,plain,
% 1.74/1.96 (b(elem!1, z)),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1567, 2161, 2153])).
% 1.74/1.96 tff(2163,plain,
% 1.74/1.96 (s(elem!1) = s(s(s(s(z))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2142])).
% 1.74/1.96 tff(2164,plain,
% 1.74/1.96 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2163])).
% 1.74/1.96 tff(2165,plain,
% 1.74/1.96 (s(s(s(elem!1))) = s(s(s(s(s(s(z))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2164])).
% 1.74/1.96 tff(2166,plain,
% 1.74/1.96 (s(s(s(s(s(s(z)))))) = s(s(s(elem!1)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2165])).
% 1.74/1.96 tff(2167,plain,
% 1.74/1.96 (s(s(s(z))) = elem!1),
% 1.74/1.96 inference(symmetry,[status(thm)],[2142])).
% 1.74/1.96 tff(2168,plain,
% 1.74/1.96 (r(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2167, 2166])).
% 1.74/1.96 tff(2169,plain,
% 1.74/1.96 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2168])).
% 1.74/1.96 tff(2170,plain,
% 1.74/1.96 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2169])).
% 1.74/1.96 tff(2171,plain,
% 1.74/1.96 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1660, 2160, 96, 2152])).
% 1.74/1.96 tff(2172,plain,
% 1.74/1.96 (~r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 1.74/1.96 tff(2173,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2166])).
% 1.74/1.96 tff(2174,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2173])).
% 1.74/1.96 tff(2175,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2174])).
% 1.74/1.96 tff(2176,plain,
% 1.74/1.96 (~(s(elem!1) = s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[922, 2151])).
% 1.74/1.96 tff(2177,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.96 tff(2178,plain,
% 1.74/1.96 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2177])).
% 1.74/1.96 tff(2179,plain,
% 1.74/1.96 (s(s(z)) = s(s(elem!1))),
% 1.74/1.96 inference(transitivity,[status(thm)],[341, 2178, 812])).
% 1.74/1.96 tff(2180,plain,
% 1.74/1.96 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2179])).
% 1.74/1.96 tff(2181,plain,
% 1.74/1.96 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.74/1.96 inference(symmetry,[status(thm)],[2180])).
% 1.74/1.96 tff(2182,plain,
% 1.74/1.96 (s(elem!1) = s(z)),
% 1.74/1.96 inference(transitivity,[status(thm)],[1003, 2181, 70])).
% 1.74/1.96 tff(2183,plain,
% 1.74/1.96 ($false),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[701, 2182])).
% 1.74/1.96 tff(2184,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.96 tff(2185,plain,
% 1.74/1.96 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2184, 2176])).
% 1.74/1.96 tff(2186,plain,
% 1.74/1.96 (~(s(s(s(z))) = s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2185, 2175])).
% 1.74/1.96 tff(2187,plain,
% 1.74/1.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(rewrite,[status(thm)],[])).
% 1.74/1.96 tff(2188,plain,
% 1.74/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z))))))))),
% 1.74/1.96 inference(quant_inst,[status(thm)],[])).
% 1.74/1.96 tff(2189,plain,
% 1.74/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 1.74/1.96 tff(2190,plain,
% 1.74/1.96 ((s(s(s(z))) = s(s(s(s(s(s(z))))))) | b(s(s(s(z))), s(s(s(s(s(s(z))))))) | r(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2189, 25])).
% 1.74/1.96 tff(2191,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(s(s(z)))))))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[2190, 2186, 2172])).
% 1.74/1.96 tff(2192,plain,
% 1.74/1.96 (b(z, s(elem!1)) <=> b(z, s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2163])).
% 1.74/1.96 tff(2193,plain,
% 1.74/1.96 (~(s(z) = s(elem!1))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1539, 2176])).
% 1.74/1.96 tff(2194,plain,
% 1.74/1.96 (b(s(s(s(z))), s(s(s(s(s(s(z))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2167, 2166])).
% 1.74/1.96 tff(2195,assumption,(b(s(s(s(z))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.74/1.96 tff(2196,plain,
% 1.74/1.96 (b(elem!1, s(s(s(elem!1))))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 1.74/1.96 tff(2197,plain,
% 1.74/1.96 (~r(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[1376, 638, 96, 95])).
% 1.74/1.96 tff(2198,plain,
% 1.74/1.96 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(z)))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2156])).
% 1.74/1.96 tff(2199,plain,
% 1.74/1.96 (~(elem!1 = s(z))),
% 1.74/1.96 inference(modus_ponens,[status(thm)],[344, 2198])).
% 1.74/1.96 tff(2200,plain,
% 1.74/1.96 (b(elem!1, s(z))),
% 1.74/1.96 inference(unit_resolution,[status(thm)],[687, 2199, 2197])).
% 1.74/1.96 tff(2201,plain,
% 1.74/1.96 ((s(s(z)) = s(elem!1)) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.74/1.96 inference(monotonicity,[status(thm)],[2163])).
% 1.74/1.96 tff(2202,plain,
% 1.74/1.96 ((s(s(z)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.74/1.96 inference(transitivity,[status(thm)],[2201, 353])).
% 1.74/1.97 tff(2203,plain,
% 1.74/1.97 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.74/1.97 inference(symmetry,[status(thm)],[2202])).
% 1.74/1.97 tff(2204,plain,
% 1.74/1.97 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2203])).
% 1.74/1.97 tff(2205,plain,
% 1.74/1.97 (~(s(s(z)) = s(elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[355, 2204])).
% 1.74/1.97 tff(2206,plain,
% 1.74/1.97 (~r(s(s(s(elem!1))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1801, 1570, 96, 259, 1, 95, 2205, 2176, 2200, 638, 2159, 1596])).
% 1.74/1.97 tff(2207,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1807, 2206])).
% 1.74/1.97 tff(2208,plain,
% 1.74/1.97 (b(s(s(z)), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1416, 1570, 2116])).
% 1.74/1.97 tff(2209,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.97 tff(2210,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2211,plain,
% 1.74/1.97 (((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2212,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2211])).
% 1.74/1.97 tff(2213,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2212, 2210])).
% 1.74/1.97 tff(2214,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2215,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2214, 2213])).
% 1.74/1.97 tff(2216,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2215, 171, 1809, 679, 259, 666, 2209])).
% 1.74/1.97 tff(2217,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2218,plain,
% 1.74/1.97 (~b(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2217, 2207, 259, 2200, 2208])).
% 1.74/1.97 tff(2219,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.74/1.97 tff(2220,plain,
% 1.74/1.97 (s(s(s(elem!1))) = s(z)),
% 1.74/1.97 inference(symmetry,[status(thm)],[2219])).
% 1.74/1.97 tff(2221,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[818, 2220])).
% 1.74/1.97 tff(2222,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2223,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.97 tff(2224,assumption,(~r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.97 tff(2225,plain,
% 1.74/1.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2226,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2227,plain,
% 1.74/1.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2226, 2225])).
% 1.74/1.97 tff(2228,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2227, 25, 2224, 2223, 2222])).
% 1.74/1.97 tff(2229,plain,(r(s(z), s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2230,plain,
% 1.74/1.97 (r(s(z), s(s(s(elem!1))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2229, 2218])).
% 1.74/1.97 tff(2231,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.74/1.97 tff(2232,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2233,plain,
% 1.74/1.97 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2234,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2233])).
% 1.74/1.97 tff(2235,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2234, 2232])).
% 1.74/1.97 tff(2236,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2237,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 1.74/1.97 tff(2238,plain,
% 1.74/1.97 (~r(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2237, 106, 96, 1663, 2231])).
% 1.74/1.97 tff(2239,plain,
% 1.74/1.97 (b(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1679, 2238])).
% 1.74/1.97 tff(2240,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2241,plain,
% 1.74/1.97 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2242,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2241])).
% 1.74/1.97 tff(2243,plain,
% 1.74/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2242, 2240])).
% 1.74/1.97 tff(2244,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2245,plain,
% 1.74/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2244, 2243])).
% 1.74/1.97 tff(2246,plain,
% 1.74/1.97 (~r(s(elem!1), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2245, 106, 96, 1663, 2231])).
% 1.74/1.97 tff(2247,plain,
% 1.74/1.97 (b(s(elem!1), z)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1691, 2246])).
% 1.74/1.97 tff(2248,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2249,plain,
% 1.74/1.97 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2250,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2249])).
% 1.74/1.97 tff(2251,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2250, 2248])).
% 1.74/1.97 tff(2252,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2253,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2252, 2251])).
% 1.74/1.97 tff(2254,plain,
% 1.74/1.97 ($false),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2253, 171, 1596, 2247, 666, 2239, 1])).
% 1.74/1.97 tff(2255,plain,((~r(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.97 tff(2256,plain,
% 1.74/1.97 (~r(s(elem!1), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2255, 2230, 96, 1, 1596, 2208])).
% 1.74/1.97 tff(2257,plain,
% 1.74/1.97 (b(s(elem!1), s(z))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1717, 2256, 2176])).
% 1.74/1.97 tff(2258,plain,
% 1.74/1.97 (~b(s(z), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1842, 2257, 2200, 2207, 2196])).
% 1.74/1.97 tff(2259,plain,
% 1.74/1.97 (r(s(z), s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1861, 2258, 2193])).
% 1.74/1.97 tff(2260,plain,
% 1.74/1.97 ((s(elem!1) = elem!1) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2163, 2142])).
% 1.74/1.97 tff(2261,plain,
% 1.74/1.97 ((s(elem!1) = elem!1) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2260, 1125])).
% 1.74/1.97 tff(2262,plain,
% 1.74/1.97 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(elem!1) = elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[2261])).
% 1.74/1.97 tff(2263,plain,
% 1.74/1.97 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(elem!1) = elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2262])).
% 1.74/1.97 tff(2264,plain,
% 1.74/1.97 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1082, 355])).
% 1.74/1.97 tff(2265,plain,
% 1.74/1.97 (~(s(elem!1) = elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2264, 2263])).
% 1.74/1.97 tff(2266,plain,
% 1.74/1.97 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2163, 2142])).
% 1.74/1.97 tff(2267,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(elem!1), elem!1)),
% 1.74/1.97 inference(symmetry,[status(thm)],[2266])).
% 1.74/1.97 tff(2268,plain,
% 1.74/1.97 ((~b(s(s(s(s(z)))), s(s(s(z))))) <=> (~b(s(elem!1), elem!1))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2267])).
% 1.74/1.97 tff(2269,plain,
% 1.74/1.97 (b(s(elem!1), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2163])).
% 1.74/1.97 tff(2270,plain,
% 1.74/1.97 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2257, 2269])).
% 1.74/1.97 tff(2271,plain,
% 1.74/1.97 (~b(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[365, 2270, 259, 356])).
% 1.74/1.97 tff(2272,plain,
% 1.74/1.97 (r(s(z), s(s(z)))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[550, 2271])).
% 1.74/1.97 tff(2273,plain,
% 1.74/1.97 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[608, 2272, 95, 600])).
% 1.74/1.97 tff(2274,plain,
% 1.74/1.97 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[351, 2273])).
% 1.74/1.97 tff(2275,plain,
% 1.74/1.97 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(z))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2142])).
% 1.74/1.97 tff(2276,plain,
% 1.74/1.97 (b(s(s(z)), s(s(s(z))))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2208, 2275])).
% 1.74/1.97 tff(2277,plain,
% 1.74/1.97 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2165])).
% 1.74/1.97 tff(2278,plain,
% 1.74/1.97 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2207, 2277])).
% 1.74/1.97 tff(2279,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2280,plain,
% 1.74/1.97 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(rewrite,[status(thm)],[])).
% 1.74/1.97 tff(2281,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))))),
% 1.74/1.97 inference(monotonicity,[status(thm)],[2280])).
% 1.74/1.97 tff(2282,plain,
% 1.74/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z))))),
% 1.74/1.97 inference(transitivity,[status(thm)],[2281, 2279])).
% 1.74/1.97 tff(2283,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), 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(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.74/1.97 inference(quant_inst,[status(thm)],[])).
% 1.74/1.97 tff(2284,plain,
% 1.74/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(z)))),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2283, 2282])).
% 1.74/1.97 tff(2285,plain,
% 1.74/1.97 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2284, 171, 2278, 2270, 2276, 2195])).
% 1.74/1.97 tff(2286,plain,
% 1.74/1.97 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[2285, 2274])).
% 1.74/1.97 tff(2287,plain,
% 1.74/1.97 (~b(s(elem!1), elem!1)),
% 1.74/1.97 inference(modus_ponens,[status(thm)],[2286, 2268])).
% 1.74/1.97 tff(2288,plain,
% 1.74/1.97 (r(s(elem!1), elem!1)),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1523, 2287, 2265])).
% 1.74/1.97 tff(2289,plain,
% 1.74/1.97 (~r(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1869, 2288, 95, 2259])).
% 1.74/1.97 tff(2290,plain,
% 1.74/1.97 (b(z, s(elem!1))),
% 1.74/1.97 inference(unit_resolution,[status(thm)],[1679, 2289])).
% 1.74/1.97 tff(2291,plain,
% 1.74/1.98 (b(z, s(s(s(s(z)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2290, 2192])).
% 1.74/1.98 tff(2292,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2293,plain,
% 1.74/1.98 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2294,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2293])).
% 1.74/1.98 tff(2295,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2294, 2292])).
% 1.74/1.98 tff(2296,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2297,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2296, 2295])).
% 1.74/1.98 tff(2298,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2297, 171, 259, 1, 2270, 356, 2291, 2141])).
% 1.74/1.98 tff(2299,plain,(r(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(s(s(z))))) | (~r(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(elem!1, z)) | (~r(z, elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2300,plain,
% 1.74/1.98 (r(s(s(z)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2299, 2142, 1, 356, 2141, 259, 95, 2191, 600, 96, 2162, 2152, 2116])).
% 1.74/1.98 tff(2301,plain,
% 1.74/1.98 (~r(s(z), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1411, 2300, 96, 600])).
% 1.74/1.98 tff(2302,plain,
% 1.74/1.98 (b(s(z), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[550, 2301])).
% 1.74/1.98 tff(2303,plain,
% 1.74/1.98 (~b(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[365, 2302, 259, 356])).
% 1.74/1.98 tff(2304,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[321, 2303, 255])).
% 1.74/1.98 tff(2305,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2306,plain,
% 1.74/1.98 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2307,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2306])).
% 1.74/1.98 tff(2308,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2307, 2305])).
% 1.74/1.98 tff(2309,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2310,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 1.74/1.98 tff(2311,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2310, 106, 260, 502, 1998, 263])).
% 1.74/1.98 tff(2312,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2313,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2312, 2304, 260, 2146])).
% 1.74/1.98 tff(2314,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[479, 2313])).
% 1.74/1.98 tff(2315,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2316,plain,
% 1.74/1.98 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2317,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2316])).
% 1.74/1.98 tff(2318,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2317, 2315])).
% 1.74/1.98 tff(2319,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2320,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2319, 2318])).
% 1.74/1.98 tff(2321,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2320, 106, 260, 126, 1357, 263])).
% 1.74/1.98 tff(2322,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2323,plain,
% 1.74/1.98 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2322, 2304, 126, 260])).
% 1.74/1.98 tff(2324,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1368, 2323])).
% 1.74/1.98 tff(2325,plain,
% 1.74/1.98 (r(elem!1, s(z)) <=> r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2142])).
% 1.74/1.98 tff(2326,plain,
% 1.74/1.98 ((~r(elem!1, s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2325])).
% 1.74/1.98 tff(2327,plain,
% 1.74/1.98 (~r(elem!1, s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1376, 2152, 96, 95])).
% 1.74/1.98 tff(2328,plain,
% 1.74/1.98 (~r(s(s(s(z))), s(z))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2327, 2326])).
% 1.74/1.98 tff(2329,plain,
% 1.74/1.98 (b(s(s(s(z))), s(z))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1171, 25, 344, 2328])).
% 1.74/1.98 tff(2330,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1220, 171, 2302, 259, 2329, 2324, 2314])).
% 1.74/1.98 tff(2331,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (s(s(z)) = elem!1) | b(s(z), elem!1) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2332,plain,
% 1.74/1.98 (~(elem!1 = s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2331, 2141, 260, 126, 2117, 94, 600, 1, 259, 95, 2116, 1427, 258])).
% 1.74/1.98 tff(2333,plain,
% 1.74/1.98 (r(elem!1, s(s(s(z))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2112, 2332])).
% 1.74/1.98 tff(2334,plain,
% 1.74/1.98 (b(s(s(z)), elem!1)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1461, 2333, 95, 84, 258, 259, 1427])).
% 1.74/1.98 tff(2335,plain,
% 1.74/1.98 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[608, 554, 95, 600])).
% 1.74/1.98 tff(2336,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(s(z)))))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[351, 2335])).
% 1.74/1.98 tff(2337,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1435])).
% 1.74/1.98 tff(2338,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2337])).
% 1.74/1.98 tff(2339,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2083])).
% 1.74/1.98 tff(2340,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2339])).
% 1.74/1.98 tff(2341,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 1.74/1.98 inference(symmetry,[status(thm)],[2340])).
% 1.74/1.98 tff(2342,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2341, 2338])).
% 1.74/1.98 tff(2343,plain,
% 1.74/1.98 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2342])).
% 1.74/1.98 tff(2344,plain,
% 1.74/1.98 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2339])).
% 1.74/1.98 tff(2345,plain,
% 1.74/1.98 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2344])).
% 1.74/1.98 tff(2346,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2345])).
% 1.74/1.98 tff(2347,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2346])).
% 1.74/1.98 tff(2348,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2339])).
% 1.74/1.98 tff(2349,plain,
% 1.74/1.98 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[83, 2348])).
% 1.74/1.98 tff(2350,plain,
% 1.74/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2349, 2347])).
% 1.74/1.98 tff(2351,plain,
% 1.74/1.98 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2082, 2339])).
% 1.74/1.98 tff(2352,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.98 tff(2353,plain,
% 1.74/1.98 (b(s(elem!1), s(s(s(elem!1))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 1.74/1.98 tff(2354,plain,
% 1.74/1.98 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2082])).
% 1.74/1.98 tff(2355,plain,
% 1.74/1.98 (b(s(elem!1), elem!1)),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[666, 2354])).
% 1.74/1.98 tff(2356,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2082])).
% 1.74/1.98 tff(2357,plain,
% 1.74/1.98 (elem!1 = s(z)),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1439, 1435])).
% 1.74/1.98 tff(2358,plain,
% 1.74/1.98 (s(elem!1) = s(s(z))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1428])).
% 1.74/1.98 tff(2359,plain,
% 1.74/1.98 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2358])).
% 1.74/1.98 tff(2360,plain,
% 1.74/1.98 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2359])).
% 1.74/1.98 tff(2361,plain,
% 1.74/1.98 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2360])).
% 1.74/1.98 tff(2362,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2361])).
% 1.74/1.98 tff(2363,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2362])).
% 1.74/1.98 tff(2364,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[991, 2363])).
% 1.74/1.98 tff(2365,plain,
% 1.74/1.98 ($false),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[368, 2364])).
% 1.74/1.98 tff(2366,plain,((~r(s(s(s(elem!1))), s(s(z)))) | r(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.98 tff(2367,plain,
% 1.74/1.98 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2366, 2357, 368])).
% 1.74/1.98 tff(2368,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(s(z)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[1013, 2367])).
% 1.74/1.98 tff(2369,plain,
% 1.74/1.98 (b(s(s(s(elem!1))), s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2368, 2356])).
% 1.74/1.98 tff(2370,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2371,plain,
% 1.74/1.98 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2372,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2371])).
% 1.74/1.98 tff(2373,plain,
% 1.74/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2372, 2370])).
% 1.74/1.98 tff(2374,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2375,plain,
% 1.74/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2374, 2373])).
% 1.74/1.98 tff(2376,plain,
% 1.74/1.98 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2375, 171, 2369, 2355, 2353])).
% 1.74/1.98 tff(2377,plain,
% 1.74/1.98 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2376, 2350])).
% 1.74/1.98 tff(2378,plain,
% 1.74/1.98 (s(elem!1) = s(s(z))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2082])).
% 1.74/1.98 tff(2379,plain,
% 1.74/1.98 ((s(s(s(s(elem!1)))) = s(elem!1)) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2345, 2378])).
% 1.74/1.98 tff(2380,plain,
% 1.74/1.98 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2379])).
% 1.74/1.98 tff(2381,plain,
% 1.74/1.98 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(elem!1)))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2380])).
% 1.74/1.98 tff(2382,plain,
% 1.74/1.98 (~(s(s(s(s(elem!1)))) = s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[196, 2381])).
% 1.74/1.98 tff(2383,plain,
% 1.74/1.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2384,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.98 tff(2385,plain,
% 1.74/1.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(elem!1)) | b(s(s(s(s(elem!1)))), s(elem!1)) | r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2384, 2383])).
% 1.74/1.98 tff(2386,plain,
% 1.74/1.98 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/1.98 inference(unit_resolution,[status(thm)],[2385, 25, 2382, 2377])).
% 1.74/1.98 tff(2387,plain,
% 1.74/1.98 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2339, 2344])).
% 1.74/1.98 tff(2388,plain,
% 1.74/1.98 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[260, 2387])).
% 1.74/1.98 tff(2389,plain,
% 1.74/1.98 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2345])).
% 1.74/1.98 tff(2390,plain,
% 1.74/1.98 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(symmetry,[status(thm)],[2389])).
% 1.74/1.98 tff(2391,plain,
% 1.74/1.98 (r(s(z), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[1435])).
% 1.74/1.98 tff(2392,plain,
% 1.74/1.98 (r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[126, 2391])).
% 1.74/1.98 tff(2393,plain,
% 1.74/1.98 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.74/1.98 inference(modus_ponens,[status(thm)],[2392, 2390])).
% 1.74/1.98 tff(2394,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2395,plain,
% 1.74/1.98 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(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(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(rewrite,[status(thm)],[])).
% 1.74/1.98 tff(2396,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.74/1.98 inference(monotonicity,[status(thm)],[2395])).
% 1.74/1.98 tff(2397,plain,
% 1.74/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.98 inference(transitivity,[status(thm)],[2396, 2394])).
% 1.74/1.98 tff(2398,plain,
% 1.74/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.74/1.98 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2399,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2398, 2397])).
% 1.74/1.99 tff(2400,plain,
% 1.74/1.99 (~r(s(s(s(elem!1))), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2399, 106, 2393, 2388, 2386])).
% 1.74/1.99 tff(2401,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2400, 2343])).
% 1.74/1.99 tff(2402,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[321, 2401, 255])).
% 1.74/1.99 tff(2403,plain,
% 1.74/1.99 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[1435])).
% 1.74/1.99 tff(2404,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(z))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2403])).
% 1.74/1.99 tff(2405,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2339])).
% 1.74/1.99 tff(2406,plain,
% 1.74/1.99 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2405])).
% 1.74/1.99 tff(2407,plain,
% 1.74/1.99 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2406, 2404])).
% 1.74/1.99 tff(2408,plain,
% 1.74/1.99 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(z), s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2407])).
% 1.74/1.99 tff(2409,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2410,plain,
% 1.74/1.99 (((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2411,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2410])).
% 1.74/1.99 tff(2412,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2411, 2409])).
% 1.74/1.99 tff(2413,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2414,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 1.74/1.99 tff(2415,plain,
% 1.74/1.99 (~r(elem!1, s(s(s(elem!1))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2414, 106, 2393, 2388, 2386])).
% 1.74/1.99 tff(2416,plain,
% 1.74/1.99 (~r(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2415, 2408])).
% 1.74/1.99 tff(2417,plain,
% 1.74/1.99 (b(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[454, 2416, 254])).
% 1.74/1.99 tff(2418,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[566, 2417, 2402, 259, 2117])).
% 1.74/1.99 tff(2419,plain,((~(s(z) = elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2420,plain,
% 1.74/1.99 (~(s(z) = elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2419, 2336, 260, 259, 83, 666, 126, 368])).
% 1.74/1.99 tff(2421,plain,
% 1.74/1.99 (r(s(z), elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1444, 2420, 1427])).
% 1.74/1.99 tff(2422,plain,
% 1.74/1.99 (~r(z, elem!1)),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[1454, 2421, 95, 1426])).
% 1.74/1.99 tff(2423,plain,
% 1.74/1.99 (z = elem!1),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[651, 2422, 258])).
% 1.74/1.99 tff(2424,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2423])).
% 1.74/1.99 tff(2425,plain,
% 1.74/1.99 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.99 inference(commutativity,[status(thm)],[])).
% 1.74/1.99 tff(2426,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2425])).
% 1.74/1.99 tff(2427,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2423])).
% 1.74/1.99 tff(2428,plain,
% 1.74/1.99 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2427, 2426])).
% 1.74/1.99 tff(2429,plain,
% 1.74/1.99 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2428])).
% 1.74/1.99 tff(2430,plain,
% 1.74/1.99 (~(elem!1 = s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[52, 2429])).
% 1.74/1.99 tff(2431,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2423])).
% 1.74/1.99 tff(2432,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), elem!1)),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2141, 2431])).
% 1.74/1.99 tff(2433,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.99 tff(2434,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2435,plain,
% 1.74/1.99 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2436,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2435])).
% 1.74/1.99 tff(2437,plain,
% 1.74/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2436, 2434])).
% 1.74/1.99 tff(2438,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2439,plain,
% 1.74/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2438, 2437])).
% 1.74/1.99 tff(2440,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2439, 171, 666, 2433, 1086, 356])).
% 1.74/1.99 tff(2441,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2442,plain,
% 1.74/1.99 (~b(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2441, 2432, 666, 2117])).
% 1.74/1.99 tff(2443,plain,
% 1.74/1.99 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2444,plain,
% 1.74/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2445,plain,
% 1.74/1.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2444, 2443])).
% 1.74/1.99 tff(2446,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2445, 25, 2442, 2430])).
% 1.74/1.99 tff(2447,plain,
% 1.74/1.99 (r(elem!1, s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[691, 2423, 84])).
% 1.74/1.99 tff(2448,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.74/1.99 tff(2449,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2450,plain,
% 1.74/1.99 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2451,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2450])).
% 1.74/1.99 tff(2452,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2451, 2449])).
% 1.74/1.99 tff(2453,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2454,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2453, 2452])).
% 1.74/1.99 tff(2455,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2454, 106, 554, 730, 263, 2448])).
% 1.74/1.99 tff(2456,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2457,plain,
% 1.74/1.99 (~r(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2456, 554, 2447, 2446])).
% 1.74/1.99 tff(2458,plain,
% 1.74/1.99 (b(s(s(s(s(z)))), s(z))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[321, 2457, 255])).
% 1.74/1.99 tff(2459,plain,
% 1.74/1.99 (~b(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[566, 2458, 259, 2117])).
% 1.74/1.99 tff(2460,plain,
% 1.74/1.99 (r(s(z), s(s(s(s(z)))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[454, 2459, 254])).
% 1.74/1.99 tff(2461,plain,
% 1.74/1.99 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2423])).
% 1.74/1.99 tff(2462,plain,
% 1.74/1.99 (r(elem!1, s(s(z)))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[600, 2461])).
% 1.74/1.99 tff(2463,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 1.74/1.99 tff(2464,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2465,plain,
% 1.74/1.99 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2466,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2465])).
% 1.74/1.99 tff(2467,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2466, 2464])).
% 1.74/1.99 tff(2468,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2469,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 1.74/1.99 tff(2470,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2469, 106, 554, 730, 2463, 501])).
% 1.74/1.99 tff(2471,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2472,plain,
% 1.74/1.99 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2471, 554, 2447, 2462])).
% 1.74/1.99 tff(2473,plain,
% 1.74/1.99 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[205, 2472])).
% 1.74/1.99 tff(2474,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[672])).
% 1.74/1.99 tff(2475,plain,
% 1.74/1.99 (b(elem!1, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(symmetry,[status(thm)],[2474])).
% 1.74/1.99 tff(2476,plain,
% 1.74/1.99 (b(z, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[840, 2475])).
% 1.74/1.99 tff(2477,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[492, 2476])).
% 1.74/1.99 tff(2478,plain,((~b(elem!1, s(s(s(s(s(z))))))) | b(z, s(s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/1.99 tff(2479,plain,
% 1.74/1.99 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2478, 492, 672])).
% 1.74/1.99 tff(2480,plain,
% 1.74/1.99 (r(elem!1, s(s(s(s(s(z))))))),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[782, 2479, 1895])).
% 1.74/1.99 tff(2481,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2482,plain,
% 1.74/1.99 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.99 inference(rewrite,[status(thm)],[])).
% 1.74/1.99 tff(2483,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.74/1.99 inference(monotonicity,[status(thm)],[2482])).
% 1.74/1.99 tff(2484,plain,
% 1.74/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.74/1.99 inference(transitivity,[status(thm)],[2483, 2481])).
% 1.74/1.99 tff(2485,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.74/1.99 inference(quant_inst,[status(thm)],[])).
% 1.74/1.99 tff(2486,plain,
% 1.74/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.74/1.99 inference(modus_ponens,[status(thm)],[2485, 2484])).
% 1.74/1.99 tff(2487,plain,
% 1.74/1.99 ($false),
% 1.74/1.99 inference(unit_resolution,[status(thm)],[2486, 106, 260, 769, 396, 2448])).
% 1.74/2.00 tff(2488,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2489,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2488, 2480, 260, 2448])).
% 1.74/2.00 tff(2490,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[225, 2489])).
% 1.74/2.00 tff(2491,plain,
% 1.74/2.00 (r(z, s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[498, 492])).
% 1.74/2.00 tff(2492,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2493,plain,
% 1.74/2.00 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2494,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2493])).
% 1.74/2.00 tff(2495,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2494, 2492])).
% 1.74/2.00 tff(2496,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2497,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2496, 2495])).
% 1.74/2.00 tff(2498,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2497, 106, 96, 502, 3, 1288])).
% 1.74/2.00 tff(2499,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2500,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2499, 2491, 96, 3])).
% 1.74/2.00 tff(2501,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[479, 2500])).
% 1.74/2.00 tff(2502,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2503,plain,
% 1.74/2.00 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2504,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2503])).
% 1.74/2.00 tff(2505,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2504, 2502])).
% 1.74/2.00 tff(2506,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2507,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2506, 2505])).
% 1.74/2.00 tff(2508,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2507, 171, 83, 2501, 160, 2490, 357, 356])).
% 1.74/2.00 tff(2509,plain,(b(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(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2510,plain,
% 1.74/2.00 (b(z, s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2509, 2473, 83, 2458, 2117, 260, 2446, 94, 2460, 2423])).
% 1.74/2.00 tff(2511,plain,
% 1.74/2.00 (b(elem!1, s(s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2510, 2424])).
% 1.74/2.00 tff(2512,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2513,plain,
% 1.74/2.00 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2514,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2513])).
% 1.74/2.00 tff(2515,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2514, 2512])).
% 1.74/2.00 tff(2516,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2517,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 1.74/2.00 tff(2518,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2517, 171, 666, 83, 840, 1086, 356, 2352])).
% 1.74/2.00 tff(2519,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2520,plain,
% 1.74/2.00 (~b(elem!1, s(s(s(s(s(z))))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2519, 2432, 83, 666, 2117, 2336])).
% 1.74/2.00 tff(2521,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2520, 2511])).
% 1.74/2.00 tff(2522,plain,((~r(s(z), s(s(z)))) | (~b(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(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | b(z, s(z)) | b(z, elem!1) | (~r(s(z), z)) | (~r(elem!1, s(s(s(z))))) | b(s(z), elem!1) | (~r(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2523,plain,
% 1.74/2.00 (~r(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2522, 2334, 83, 260, 259, 2141, 600, 84, 258, 95, 2333, 1427, 126, 368])).
% 1.74/2.00 tff(2524,plain,
% 1.74/2.00 (b(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[550, 2523])).
% 1.74/2.00 tff(2525,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[365, 2524, 259, 2117])).
% 1.74/2.00 tff(2526,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[321, 2525, 255])).
% 1.74/2.00 tff(2527,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 1.74/2.00 tff(2528,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2529,plain,
% 1.74/2.00 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2530,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2529])).
% 1.74/2.00 tff(2531,plain,
% 1.74/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2530, 2528])).
% 1.74/2.00 tff(2532,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2533,plain,
% 1.74/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2532, 2531])).
% 1.74/2.00 tff(2534,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2533, 171, 1, 356, 2527, 2141])).
% 1.74/2.00 tff(2535,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2536,plain,
% 1.74/2.00 (~b(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2535, 2141, 2117, 1])).
% 1.74/2.00 tff(2537,plain,
% 1.74/2.00 (r(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[293, 2536])).
% 1.74/2.00 tff(2538,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[281, 106, 94, 95, 2537, 2526])).
% 1.74/2.00 tff(2539,plain,((~b(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | b(z, s(z)) | b(z, elem!1) | b(s(z), elem!1) | (~r(s(z), s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(z))) | (~b(s(s(z)), z)) | b(elem!1, s(s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2540,plain,
% 1.74/2.00 (~b(s(s(z)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2539, 2140, 259, 83, 260, 600, 84, 258, 1427, 126, 368, 95, 946, 2116])).
% 1.74/2.00 tff(2541,plain,
% 1.74/2.00 (r(s(s(z)), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[157, 2540])).
% 1.74/2.00 tff(2542,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2543,plain,
% 1.74/2.00 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(rewrite,[status(thm)],[])).
% 1.74/2.00 tff(2544,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2543])).
% 1.74/2.00 tff(2545,plain,
% 1.74/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.74/2.00 inference(transitivity,[status(thm)],[2544, 2542])).
% 1.74/2.00 tff(2546,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.74/2.00 inference(quant_inst,[status(thm)],[])).
% 1.74/2.00 tff(2547,plain,
% 1.74/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2546, 2545])).
% 1.74/2.00 tff(2548,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2547, 106, 554, 96, 637, 600])).
% 1.74/2.00 tff(2549,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2550,plain,
% 1.74/2.00 (~r(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2549, 2541, 94, 600])).
% 1.74/2.00 tff(2551,plain,
% 1.74/2.00 (b(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[550, 2550])).
% 1.74/2.00 tff(2552,plain,
% 1.74/2.00 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[365, 2551, 259, 2117])).
% 1.74/2.00 tff(2553,plain,
% 1.74/2.00 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[321, 2552, 255])).
% 1.74/2.00 tff(2554,plain,
% 1.74/2.00 (~r(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[281, 106, 94, 95, 2553])).
% 1.74/2.00 tff(2555,plain,
% 1.74/2.00 (b(z, s(s(s(s(z)))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[293, 2554])).
% 1.74/2.00 tff(2556,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[302, 2553, 126, 260])).
% 1.74/2.00 tff(2557,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[145, 2556])).
% 1.74/2.00 tff(2558,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[310, 171, 83, 2557, 2555, 2140])).
% 1.74/2.00 tff(2559,plain,((~r(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | b(z, s(z)) | b(z, elem!1) | b(s(z), elem!1) | r(s(s(s(s(z)))), s(s(z))) | b(elem!1, s(s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2560,plain,
% 1.74/2.00 (~r(z, s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2559, 2116, 95, 126, 260, 259, 84, 258, 1427, 368, 946, 83])).
% 1.74/2.00 tff(2561,plain,
% 1.74/2.00 (b(z, s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[124, 2560])).
% 1.74/2.00 tff(2562,plain,
% 1.74/2.00 (r(s(s(z)), elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1416, 733, 2116])).
% 1.74/2.00 tff(2563,plain,
% 1.74/2.00 (~r(elem!1, s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1461, 733, 95, 84, 258, 259, 1427])).
% 1.74/2.00 tff(2564,plain,
% 1.74/2.00 (elem!1 = s(s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2112, 2563])).
% 1.74/2.00 tff(2565,plain,
% 1.74/2.00 (s(s(s(z))) = elem!1),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2149, 2564])).
% 1.74/2.00 tff(2566,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(z)), elem!1)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[785])).
% 1.74/2.00 tff(2567,plain,
% 1.74/2.00 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2566])).
% 1.74/2.00 tff(2568,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1403, 2567])).
% 1.74/2.00 tff(2569,assumption,(~r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.00 tff(2570,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2569, 2568])).
% 1.74/2.00 tff(2571,plain,((~(s(s(s(z))) = elem!1)) | r(s(s(z)), s(s(s(z)))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2572,plain,
% 1.74/2.00 (r(s(s(z)), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2571, 2565, 2562])).
% 1.74/2.00 tff(2573,plain,
% 1.74/2.00 (r(s(z), elem!1) <=> r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2564])).
% 1.74/2.00 tff(2574,plain,
% 1.74/2.00 (r(s(z), s(s(s(z))))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[1445, 2573])).
% 1.74/2.00 tff(2575,plain,
% 1.74/2.00 (~(z = elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[788, 2565])).
% 1.74/2.00 tff(2576,plain,
% 1.74/2.00 (r(z, elem!1)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[651, 2575, 258])).
% 1.74/2.00 tff(2577,plain,
% 1.74/2.00 (b(elem!1, z) <=> b(s(s(s(z))), z)),
% 1.74/2.00 inference(monotonicity,[status(thm)],[2564])).
% 1.74/2.00 tff(2578,plain,
% 1.74/2.00 (~(elem!1 = z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[697, 2575])).
% 1.74/2.00 tff(2579,plain,
% 1.74/2.00 (~r(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1562, 2576, 94, 1445])).
% 1.74/2.00 tff(2580,plain,
% 1.74/2.00 (b(elem!1, z)),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1567, 2579, 2578])).
% 1.74/2.00 tff(2581,plain,
% 1.74/2.00 (b(s(s(s(z))), z)),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[2580, 2577])).
% 1.74/2.00 tff(2582,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2312, 263, 260, 2574])).
% 1.74/2.00 tff(2583,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[479, 2582])).
% 1.74/2.00 tff(2584,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2322, 263, 126, 260])).
% 1.74/2.00 tff(2585,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1368, 2584])).
% 1.74/2.00 tff(2586,plain,
% 1.74/2.00 (~r(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2312, 2574, 260, 263])).
% 1.74/2.00 tff(2587,plain,
% 1.74/2.00 (b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[479, 2586])).
% 1.74/2.00 tff(2588,plain,
% 1.74/2.00 (~r(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1376, 2576, 94, 95])).
% 1.74/2.00 tff(2589,plain,
% 1.74/2.00 (b(elem!1, s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[687, 2588, 1434])).
% 1.74/2.00 tff(2590,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z)) <=> b(elem!1, s(z))),
% 1.74/2.00 inference(monotonicity,[status(thm)],[785])).
% 1.74/2.00 tff(2591,plain,
% 1.74/2.00 (b(elem!1, s(z)) <=> b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(symmetry,[status(thm)],[2590])).
% 1.74/2.00 tff(2592,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(modus_ponens,[status(thm)],[679, 2591])).
% 1.74/2.00 tff(2593,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1168, 2592])).
% 1.74/2.00 tff(2594,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(z))), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2595,plain,
% 1.74/2.00 (b(s(s(s(z))), s(z))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2594, 2589, 2565])).
% 1.74/2.00 tff(2596,plain,
% 1.74/2.00 ($false),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[1220, 171, 323, 259, 2595, 1384, 2587])).
% 1.74/2.00 tff(2597,plain,(b(s(s(z)), elem!1) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | b(z, elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.00 tff(2598,plain,
% 1.74/2.00 (~b(s(z), s(s(z)))),
% 1.74/2.00 inference(unit_resolution,[status(thm)],[2597, 2585, 259, 733, 260, 263, 95, 258, 1427, 946, 84])).
% 1.74/2.01 tff(2599,plain,
% 1.74/2.01 (r(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[550, 2598])).
% 1.74/2.01 tff(2600,plain,
% 1.74/2.01 (~r(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[646, 2599, 2576, 95])).
% 1.74/2.01 tff(2601,plain,
% 1.74/2.01 (b(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[157, 2600])).
% 1.74/2.01 tff(2602,plain,
% 1.74/2.01 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[634, 2601, 83, 356, 161])).
% 1.74/2.01 tff(2603,plain,
% 1.74/2.01 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[225, 2602])).
% 1.74/2.01 tff(2604,assumption,(r(s(s(s(z))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.74/2.01 tff(2605,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2606,plain,
% 1.74/2.01 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2607,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2606])).
% 1.74/2.01 tff(2608,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2607, 2605])).
% 1.74/2.01 tff(2609,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2610,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2609, 2608])).
% 1.74/2.01 tff(2611,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2610, 106, 2604, 126, 1998, 396])).
% 1.74/2.01 tff(2612,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2613,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2612, 2603, 126, 2574])).
% 1.74/2.01 tff(2614,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[835, 413])).
% 1.74/2.01 tff(2615,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2614, 2613])).
% 1.74/2.01 tff(2616,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2617,plain,
% 1.74/2.01 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2618,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2617])).
% 1.74/2.01 tff(2619,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2618, 2616])).
% 1.74/2.01 tff(2620,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2621,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2620, 2619])).
% 1.74/2.01 tff(2622,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2621, 171, 259, 161, 2615, 2583, 304, 2581])).
% 1.74/2.01 tff(2623,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(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(z)))) | (~r(s(z), z)) | b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2624,plain,
% 1.74/2.01 (~r(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2623, 733, 161, 126, 83, 356, 95, 259, 260, 258, 1427, 946, 84])).
% 1.74/2.01 tff(2625,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[321, 2624, 255])).
% 1.74/2.01 tff(2626,plain,
% 1.74/2.01 (~b(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[365, 2625, 259, 356])).
% 1.74/2.01 tff(2627,plain,
% 1.74/2.01 (r(s(z), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[550, 2626])).
% 1.74/2.01 tff(2628,plain,
% 1.74/2.01 (~r(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[646, 2627, 2576, 95])).
% 1.74/2.01 tff(2629,plain,
% 1.74/2.01 (b(s(s(z)), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[157, 2628])).
% 1.74/2.01 tff(2630,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2631,plain,
% 1.74/2.01 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2632,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2631])).
% 1.74/2.01 tff(2633,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2632, 2630])).
% 1.74/2.01 tff(2634,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2635,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.74/2.01 tff(2636,plain,
% 1.74/2.01 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2635, 171, 259, 161, 2581])).
% 1.74/2.01 tff(2637,plain,
% 1.74/2.01 (~b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2636, 2629])).
% 1.74/2.01 tff(2638,plain,
% 1.74/2.01 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2639,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2640,plain,
% 1.74/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2639, 2638])).
% 1.74/2.01 tff(2641,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2640, 25, 1018, 993, 80])).
% 1.74/2.01 tff(2642,plain,(b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2643,plain,
% 1.74/2.01 (r(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2642, 2637])).
% 1.74/2.01 tff(2644,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2645,plain,
% 1.74/2.01 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2646,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2645])).
% 1.74/2.01 tff(2647,plain,
% 1.74/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2646, 2644])).
% 1.74/2.01 tff(2648,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2649,plain,
% 1.74/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2648, 2647])).
% 1.74/2.01 tff(2650,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2649, 106, 2627, 2643, 2574, 2572])).
% 1.74/2.01 tff(2651,plain,(b(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2652,plain,
% 1.74/2.01 (b(s(s(z)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2651, 2561, 259, 95, 2117, 126, 83, 260, 258, 1427, 946, 84, 2116])).
% 1.74/2.01 tff(2653,plain,
% 1.74/2.01 (~b(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[669, 2652, 258, 95, 83, 2117, 2561, 126, 260, 259])).
% 1.74/2.01 tff(2654,plain,
% 1.74/2.01 (r(s(s(s(s(z)))), s(z))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[321, 2653, 255])).
% 1.74/2.01 tff(2655,plain,
% 1.74/2.01 (~r(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[266, 106, 94, 95, 2654])).
% 1.74/2.01 tff(2656,plain,
% 1.74/2.01 (b(s(s(s(s(z)))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[274, 2655])).
% 1.74/2.01 tff(2657,plain,
% 1.74/2.01 (~r(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[281, 106, 94, 95, 2654])).
% 1.74/2.01 tff(2658,plain,
% 1.74/2.01 (b(z, s(s(s(s(z)))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[293, 2657])).
% 1.74/2.01 tff(2659,plain,
% 1.74/2.01 (~r(s(s(s(s(s(z))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[302, 2654, 126, 260])).
% 1.74/2.01 tff(2660,plain,
% 1.74/2.01 (b(s(s(s(s(s(z))))), z)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[145, 2659])).
% 1.74/2.01 tff(2661,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2662,plain,
% 1.74/2.01 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.01 inference(rewrite,[status(thm)],[])).
% 1.74/2.01 tff(2663,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2662])).
% 1.74/2.01 tff(2664,plain,
% 1.74/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.74/2.01 inference(transitivity,[status(thm)],[2663, 2661])).
% 1.74/2.01 tff(2665,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.74/2.01 inference(quant_inst,[status(thm)],[])).
% 1.74/2.01 tff(2666,plain,
% 1.74/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 1.74/2.01 tff(2667,plain,
% 1.74/2.01 ($false),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2666, 171, 2561, 83, 2660, 2658, 2656])).
% 1.74/2.01 tff(2668,plain,((s(s(z)) = elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | (~b(s(s(z)), s(z))) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z)) | r(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.01 tff(2669,plain,
% 1.74/2.01 (r(s(s(s(s(z)))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2668, 2115, 95, 126, 260, 258, 259, 1427, 946, 84, 83])).
% 1.74/2.01 tff(2670,plain,
% 1.74/2.01 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[587, 357, 2669, 260, 259, 554])).
% 1.74/2.01 tff(2671,plain,
% 1.74/2.01 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[205, 2670])).
% 1.74/2.01 tff(2672,plain,
% 1.74/2.01 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 1.74/2.01 inference(monotonicity,[status(thm)],[2564])).
% 1.74/2.01 tff(2673,plain,
% 1.74/2.01 (r(z, s(s(s(z))))),
% 1.74/2.01 inference(modus_ponens,[status(thm)],[2576, 2672])).
% 1.74/2.01 tff(2674,plain,
% 1.74/2.01 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2006, 2574, 94, 2673])).
% 1.74/2.01 tff(2675,plain,
% 1.74/2.01 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[2642, 2674])).
% 1.74/2.01 tff(2676,plain,
% 1.74/2.01 (r(s(s(z)), elem!1)),
% 1.74/2.01 inference(unit_resolution,[status(thm)],[1416, 733, 2115])).
% 1.74/2.02 tff(2677,plain,
% 1.74/2.02 (r(s(s(z)), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2571, 2565, 2676])).
% 1.74/2.02 tff(2678,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.02 tff(2679,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2680,plain,
% 1.74/2.02 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2681,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2680])).
% 1.74/2.02 tff(2682,plain,
% 1.74/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2681, 2679])).
% 1.74/2.02 tff(2683,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2684,plain,
% 1.74/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2683, 2682])).
% 1.74/2.02 tff(2685,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2684, 106, 554, 95, 600, 2678])).
% 1.74/2.02 tff(2686,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2687,plain,
% 1.74/2.02 (~r(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2686, 2599, 2677, 95])).
% 1.74/2.02 tff(2688,plain,
% 1.74/2.02 (b(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[124, 2687])).
% 1.74/2.02 tff(2689,plain,
% 1.74/2.02 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[215, 2688, 2601, 304])).
% 1.74/2.02 tff(2690,plain,
% 1.74/2.02 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[225, 2689])).
% 1.74/2.02 tff(2691,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2612, 2690, 126, 2574])).
% 1.74/2.02 tff(2692,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2614, 2691])).
% 1.74/2.02 tff(2693,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2621, 171, 259, 2688, 2692, 2583, 304, 2581])).
% 1.74/2.02 tff(2694,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | b(s(s(z)), elem!1) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2695,plain,
% 1.74/2.02 (~r(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2694, 733, 126, 95, 259, 260, 258, 1427, 946, 84])).
% 1.74/2.02 tff(2696,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[321, 2695, 255])).
% 1.74/2.02 tff(2697,plain,
% 1.74/2.02 (~r(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[646, 637, 638, 95])).
% 1.74/2.02 tff(2698,plain,
% 1.74/2.02 (b(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[550, 2697])).
% 1.74/2.02 tff(2699,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1207, 2698, 355, 357, 1188, 259, 637])).
% 1.74/2.02 tff(2700,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2642, 2699])).
% 1.74/2.02 tff(2701,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1182, 171, 2698, 259, 1188, 2700])).
% 1.74/2.02 tff(2702,plain,((~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2703,plain,
% 1.74/2.02 (~r(s(s(z)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2702, 2696, 2595, 259, 2576, 95])).
% 1.74/2.02 tff(2704,plain,
% 1.74/2.02 (b(s(s(z)), z)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[157, 2703])).
% 1.74/2.02 tff(2705,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.74/2.02 tff(2706,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1182, 171, 323, 259, 1188, 2705])).
% 1.74/2.02 tff(2707,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2708,plain,
% 1.74/2.02 (~b(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2707, 2595, 259, 2675])).
% 1.74/2.02 tff(2709,plain,
% 1.74/2.02 (r(s(z), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[550, 2708])).
% 1.74/2.02 tff(2710,plain,
% 1.74/2.02 (~r(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2686, 2709, 2677, 95])).
% 1.74/2.02 tff(2711,plain,
% 1.74/2.02 (b(z, s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[124, 2710])).
% 1.74/2.02 tff(2712,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2635, 171, 259, 2711, 2704, 2675, 2581])).
% 1.74/2.02 tff(2713,plain,(b(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2714,plain,
% 1.74/2.02 (b(s(s(z)), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2713, 1427, 95, 126, 260, 258, 259, 946, 84])).
% 1.74/2.02 tff(2715,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2142])).
% 1.74/2.02 tff(2716,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(symmetry,[status(thm)],[2715])).
% 1.74/2.02 tff(2717,plain,
% 1.74/2.02 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2163])).
% 1.74/2.02 tff(2718,plain,
% 1.74/2.02 (b(elem!1, s(z))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[687, 2199, 676])).
% 1.74/2.02 tff(2719,plain,
% 1.74/2.02 (b(s(s(s(s(z)))), s(z)) <=> b(s(elem!1), s(z))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2269])).
% 1.74/2.02 tff(2720,plain,
% 1.74/2.02 (b(s(elem!1), s(z))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[357, 2719])).
% 1.74/2.02 tff(2721,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2722,plain,
% 1.74/2.02 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2723,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1)))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2722])).
% 1.74/2.02 tff(2724,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2723, 2721])).
% 1.74/2.02 tff(2725,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2726,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 1.74/2.02 tff(2727,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2726, 171, 679, 259, 1740, 1834, 666])).
% 1.74/2.02 tff(2728,plain,((~b(s(z), s(elem!1))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2729,plain,
% 1.74/2.02 (~b(s(z), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2728, 2720, 259, 666, 2718])).
% 1.74/2.02 tff(2730,plain,
% 1.74/2.02 (r(s(z), s(elem!1))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1861, 2729, 1858])).
% 1.74/2.02 tff(2731,plain,
% 1.74/2.02 (r(s(z), s(s(s(s(z)))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2730, 2717])).
% 1.74/2.02 tff(2732,plain,
% 1.74/2.02 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1365, 2731, 126, 260])).
% 1.74/2.02 tff(2733,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1368, 2732])).
% 1.74/2.02 tff(2734,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2733, 2716])).
% 1.74/2.02 tff(2735,plain,
% 1.74/2.02 (r(z, elem!1) <=> r(z, s(s(s(z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2142])).
% 1.74/2.02 tff(2736,plain,
% 1.74/2.02 (r(z, s(s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[638, 2735])).
% 1.74/2.02 tff(2737,plain,
% 1.74/2.02 (~r(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2006, 2146, 96, 2736])).
% 1.74/2.02 tff(2738,plain,
% 1.74/2.02 (b(s(s(s(z))), s(s(z)))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2642, 2737])).
% 1.74/2.02 tff(2739,plain,
% 1.74/2.02 (b(s(s(z)), s(s(s(z))))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[666, 2275])).
% 1.74/2.02 tff(2740,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.74/2.02 tff(2741,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2742,plain,
% 1.74/2.02 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), 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(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.02 inference(rewrite,[status(thm)],[])).
% 1.74/2.02 tff(2743,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), 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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2742])).
% 1.74/2.02 tff(2744,plain,
% 1.74/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), 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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2743, 2741])).
% 1.74/2.02 tff(2745,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), 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(z)), s(s(s(s(s(z))))))))),
% 1.74/2.02 inference(quant_inst,[status(thm)],[])).
% 1.74/2.02 tff(2746,plain,
% 1.74/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[2745, 2744])).
% 1.74/2.02 tff(2747,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2746, 171, 666, 2705, 839, 1384, 160, 2740])).
% 1.74/2.02 tff(2748,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2749,plain,
% 1.74/2.02 (~b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2748, 2733, 666, 160, 2739, 2738])).
% 1.74/2.02 tff(2750,plain,
% 1.74/2.02 ($false),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2749, 2734])).
% 1.74/2.02 tff(2751,plain,((~(elem!1 = s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (s(z) = s(elem!1)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | r(elem!1, s(z)) | (~b(s(s(s(s(z)))), s(z))) | b(s(z), elem!1) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.74/2.02 tff(2752,plain,
% 1.74/2.02 (~(elem!1 = s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2751, 1540, 160, 126, 260, 2714, 94, 259, 676, 357, 1427, 1465])).
% 1.74/2.02 tff(2753,plain,
% 1.74/2.02 (r(elem!1, s(s(s(z))))),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[2112, 2752])).
% 1.74/2.02 tff(2754,plain,
% 1.74/2.02 (~r(s(z), elem!1)),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1454, 2753, 95, 1465])).
% 1.74/2.02 tff(2755,plain,
% 1.74/2.02 (s(z) = elem!1),
% 1.74/2.02 inference(unit_resolution,[status(thm)],[1444, 2754, 1427])).
% 1.74/2.02 tff(2756,plain,
% 1.74/2.02 (s(s(z)) = s(elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2755])).
% 1.74/2.02 tff(2757,plain,
% 1.74/2.02 (s(s(s(z))) = s(s(elem!1))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2756])).
% 1.74/2.02 tff(2758,plain,
% 1.74/2.02 (s(s(elem!1)) = s(s(s(z)))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2757])).
% 1.74/2.02 tff(2759,plain,
% 1.74/2.02 (s(elem!1) = s(s(z))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2756])).
% 1.74/2.02 tff(2760,plain,
% 1.74/2.02 ((s(elem!1) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(z))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2759, 2758])).
% 1.74/2.02 tff(2761,plain,
% 1.74/2.02 ((s(elem!1) = s(s(elem!1))) <=> (s(s(s(z))) = s(s(z)))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2760, 897])).
% 1.74/2.02 tff(2762,plain,
% 1.74/2.02 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2761])).
% 1.74/2.02 tff(2763,plain,
% 1.74/2.02 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2762])).
% 1.74/2.02 tff(2764,plain,
% 1.74/2.02 (~(s(elem!1) = s(s(elem!1)))),
% 1.74/2.02 inference(modus_ponens,[status(thm)],[80, 2763])).
% 1.74/2.02 tff(2765,plain,
% 1.74/2.02 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2757])).
% 1.74/2.02 tff(2766,plain,
% 1.74/2.02 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2765])).
% 1.74/2.02 tff(2767,plain,
% 1.74/2.02 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2766])).
% 1.74/2.02 tff(2768,plain,
% 1.74/2.02 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2767, 2759])).
% 1.74/2.02 tff(2769,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2768])).
% 1.74/2.02 tff(2770,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2755])).
% 1.74/2.02 tff(2771,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.02 inference(symmetry,[status(thm)],[2770])).
% 1.74/2.02 tff(2772,plain,
% 1.74/2.02 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2766])).
% 1.74/2.02 tff(2773,plain,
% 1.74/2.02 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.74/2.02 inference(symmetry,[status(thm)],[2772])).
% 1.74/2.02 tff(2774,plain,
% 1.74/2.02 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.74/2.02 inference(transitivity,[status(thm)],[2773, 2771])).
% 1.74/2.02 tff(2775,plain,
% 1.74/2.02 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.74/2.02 inference(monotonicity,[status(thm)],[2755])).
% 1.86/2.02 tff(2776,plain,
% 1.86/2.02 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.86/2.02 inference(transitivity,[status(thm)],[2775, 1043])).
% 1.86/2.02 tff(2777,plain,
% 1.86/2.02 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.02 inference(transitivity,[status(thm)],[2776, 1044])).
% 1.86/2.02 tff(2778,plain,
% 1.86/2.02 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2777])).
% 1.86/2.02 tff(2779,plain,
% 1.86/2.02 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[726, 2778])).
% 1.86/2.02 tff(2780,plain,
% 1.86/2.02 (r(s(z), z) <=> r(elem!1, z)),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2755])).
% 1.86/2.02 tff(2781,plain,
% 1.86/2.02 (r(elem!1, z)),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[95, 2780])).
% 1.86/2.02 tff(2782,plain,
% 1.86/2.02 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2756])).
% 1.86/2.02 tff(2783,plain,
% 1.86/2.02 (b(s(elem!1), z)),
% 1.86/2.02 inference(modus_ponens,[status(thm)],[1467, 2782])).
% 1.86/2.02 tff(2784,plain,
% 1.86/2.02 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(s(s(s(z))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2345])).
% 1.86/2.02 tff(2785,plain,
% 1.86/2.02 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.86/2.02 inference(symmetry,[status(thm)],[2784])).
% 1.86/2.02 tff(2786,plain,
% 1.86/2.02 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(s(z))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2345])).
% 1.86/2.02 tff(2787,plain,
% 1.86/2.02 ((~r(z, s(s(s(s(elem!1)))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 1.86/2.02 inference(monotonicity,[status(thm)],[2786])).
% 1.86/2.02 tff(2788,plain,
% 1.86/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.86/2.02 inference(rewrite,[status(thm)],[])).
% 1.86/2.02 tff(2789,plain,
% 1.86/2.02 (((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2790,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2789])).
% 1.86/2.03 tff(2791,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2790, 2788])).
% 1.86/2.03 tff(2792,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2793,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, s(s(s(s(elem!1))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2792, 2791])).
% 1.86/2.03 tff(2794,plain,
% 1.86/2.03 (~r(z, s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2793, 106, 638, 1554, 1113])).
% 1.86/2.03 tff(2795,plain,
% 1.86/2.03 (~r(z, s(s(s(s(s(z))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2794, 2787])).
% 1.86/2.03 tff(2796,plain,
% 1.86/2.03 (b(z, s(s(s(s(s(z))))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[498, 2795])).
% 1.86/2.03 tff(2797,plain,
% 1.86/2.03 (b(z, s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2796, 2785])).
% 1.86/2.03 tff(2798,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2799,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2800,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2799, 2798])).
% 1.86/2.03 tff(2801,plain,
% 1.86/2.03 (~r(s(s(s(s(elem!1)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2800, 106, 638, 1554, 1113])).
% 1.86/2.03 tff(2802,plain,
% 1.86/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2803,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2804,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2803, 2802])).
% 1.86/2.03 tff(2805,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2804, 25, 1050, 2801])).
% 1.86/2.03 tff(2806,plain,
% 1.86/2.03 (b(s(elem!1), s(s(s(s(elem!1))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2378, 2345])).
% 1.86/2.03 tff(2807,plain,
% 1.86/2.03 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2806])).
% 1.86/2.03 tff(2808,plain,
% 1.86/2.03 (b(s(elem!1), s(s(s(s(elem!1)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[160, 2807])).
% 1.86/2.03 tff(2809,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2810,plain,
% 1.86/2.03 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2811,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2810])).
% 1.86/2.03 tff(2812,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2811, 2809])).
% 1.86/2.03 tff(2813,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2814,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), s(s(s(s(elem!1)))))) | (~b(s(elem!1), z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2813, 2812])).
% 1.86/2.03 tff(2815,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2814, 171, 1847, 2808, 2805, 2797])).
% 1.86/2.03 tff(2816,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(elem!1), z)) | (~(s(z) = elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2817,plain,
% 1.86/2.03 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2816, 2783, 2755, 160, 1465, 2781])).
% 1.86/2.03 tff(2818,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1110, 2817, 2779])).
% 1.86/2.03 tff(2819,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2818, 2774])).
% 1.86/2.03 tff(2820,plain,
% 1.86/2.03 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[445, 2819, 357, 259])).
% 1.86/2.03 tff(2821,plain,
% 1.86/2.03 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[454, 2820, 254])).
% 1.86/2.03 tff(2822,plain,
% 1.86/2.03 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[463, 2821, 126, 260])).
% 1.86/2.03 tff(2823,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[225, 2822])).
% 1.86/2.03 tff(2824,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2823, 2769])).
% 1.86/2.03 tff(2825,plain,
% 1.86/2.03 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2755])).
% 1.86/2.03 tff(2826,plain,
% 1.86/2.03 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2825])).
% 1.86/2.03 tff(2827,plain,
% 1.86/2.03 (r(s(z), s(s(s(z))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2753, 2826])).
% 1.86/2.03 tff(2828,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.03 tff(2829,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2830,plain,
% 1.86/2.03 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2831,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2830])).
% 1.86/2.03 tff(2832,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2831, 2829])).
% 1.86/2.03 tff(2833,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2834,plain,
% 1.86/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 1.86/2.03 tff(2835,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2834, 106, 260, 1998, 3, 2828])).
% 1.86/2.03 tff(2836,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2837,plain,
% 1.86/2.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2836, 2821, 260, 2827])).
% 1.86/2.03 tff(2838,assumption,(~r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.03 tff(2839,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.03 tff(2840,assumption,(~b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.03 tff(2841,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1102, 25, 2840, 2839, 2838])).
% 1.86/2.03 tff(2842,plain,(b(s(s(s(z))), s(s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2843,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2842, 2837, 2264])).
% 1.86/2.03 tff(2844,plain,
% 1.86/2.03 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2083])).
% 1.86/2.03 tff(2845,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2844])).
% 1.86/2.03 tff(2846,plain,
% 1.86/2.03 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2339])).
% 1.86/2.03 tff(2847,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2846])).
% 1.86/2.03 tff(2848,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2847, 2845])).
% 1.86/2.03 tff(2849,plain,
% 1.86/2.03 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2848])).
% 1.86/2.03 tff(2850,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.03 tff(2851,plain,
% 1.86/2.03 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2850, 2849])).
% 1.86/2.03 tff(2852,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.03 tff(2853,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2852, 2851])).
% 1.86/2.03 tff(2854,plain,(b(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2855,plain,
% 1.86/2.03 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2854, 2843, 2755])).
% 1.86/2.03 tff(2856,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2757])).
% 1.86/2.03 tff(2857,plain,
% 1.86/2.03 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1365, 2821, 126, 260])).
% 1.86/2.03 tff(2858,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1368, 2857])).
% 1.86/2.03 tff(2859,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2858, 2856])).
% 1.86/2.03 tff(2860,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(s(z))))), s(s(elem!1)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2345])).
% 1.86/2.03 tff(2861,plain,
% 1.86/2.03 (b(s(s(s(s(s(z))))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2860])).
% 1.86/2.03 tff(2862,assumption,(b(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.03 tff(2863,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 1.86/2.03 tff(2864,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.86/2.03 tff(2865,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2864, 2863])).
% 1.86/2.03 tff(2866,plain,(b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~b(s(s(s(s(s(z))))), s(s(elem!1)))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2867,plain,
% 1.86/2.03 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2866, 2859, 2755])).
% 1.86/2.03 tff(2868,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2765])).
% 1.86/2.03 tff(2869,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2755])).
% 1.86/2.03 tff(2870,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[357, 2869])).
% 1.86/2.03 tff(2871,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2870, 2868])).
% 1.86/2.03 tff(2872,plain,
% 1.86/2.03 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2756])).
% 1.86/2.03 tff(2873,plain,
% 1.86/2.03 (b(s(elem!1), elem!1)),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2714, 2872])).
% 1.86/2.03 tff(2874,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2875,plain,
% 1.86/2.03 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(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(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2876,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2875])).
% 1.86/2.03 tff(2877,plain,
% 1.86/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.86/2.03 inference(transitivity,[status(thm)],[2876, 2874])).
% 1.86/2.03 tff(2878,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), 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(s(s(elem!1)))), s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2879,plain,
% 1.86/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2878, 2877])).
% 1.86/2.03 tff(2880,plain,
% 1.86/2.03 ((~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2879, 171, 2873, 2871, 2867, 2855])).
% 1.86/2.03 tff(2881,plain,
% 1.86/2.03 (~b(s(elem!1), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2880, 2824])).
% 1.86/2.03 tff(2882,plain,
% 1.86/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2883,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.86/2.03 inference(quant_inst,[status(thm)],[])).
% 1.86/2.03 tff(2884,plain,
% 1.86/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2883, 2882])).
% 1.86/2.03 tff(2885,plain,
% 1.86/2.03 ((s(elem!1) = s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2884, 25, 2881])).
% 1.86/2.03 tff(2886,plain,
% 1.86/2.03 (r(s(elem!1), s(s(elem!1)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2885, 2764])).
% 1.86/2.03 tff(2887,plain,
% 1.86/2.03 (r(elem!1, s(s(z))) <=> r(elem!1, s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2756])).
% 1.86/2.03 tff(2888,plain,
% 1.86/2.03 (r(s(z), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2755])).
% 1.86/2.03 tff(2889,plain,
% 1.86/2.03 (r(elem!1, s(s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[554, 2888])).
% 1.86/2.03 tff(2890,plain,
% 1.86/2.03 (r(elem!1, s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2889, 2887])).
% 1.86/2.03 tff(2891,assumption,(~r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.86/2.03 tff(2892,plain,
% 1.86/2.03 (~r(s(z), s(s(s(s(z)))))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2891, 2408])).
% 1.86/2.03 tff(2893,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[3, 2892])).
% 1.86/2.03 tff(2894,plain,(r(elem!1, s(s(s(elem!1)))) | (~r(s(z), s(s(s(s(z)))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2895,plain,
% 1.86/2.03 (r(elem!1, s(s(s(elem!1))))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2894, 2821, 2755])).
% 1.86/2.03 tff(2896,plain,
% 1.86/2.03 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2756])).
% 1.86/2.03 tff(2897,plain,
% 1.86/2.03 (elem!1 = s(z)),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1439, 2755])).
% 1.86/2.03 tff(2898,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(monotonicity,[status(thm)],[2361])).
% 1.86/2.03 tff(2899,plain,
% 1.86/2.03 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.03 inference(symmetry,[status(thm)],[2898])).
% 1.86/2.03 tff(2900,plain,
% 1.86/2.03 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[1016, 2899])).
% 1.86/2.03 tff(2901,plain,
% 1.86/2.03 ($false),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[367, 2900])).
% 1.86/2.03 tff(2902,plain,((~b(s(s(s(elem!1))), s(s(z)))) | b(s(s(s(s(z)))), s(s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.03 tff(2903,plain,
% 1.86/2.03 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[2902, 2897, 367])).
% 1.86/2.03 tff(2904,plain,
% 1.86/2.03 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.03 inference(unit_resolution,[status(thm)],[1013, 2903])).
% 1.86/2.03 tff(2905,plain,
% 1.86/2.03 (r(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.03 inference(modus_ponens,[status(thm)],[2904, 2896])).
% 1.86/2.03 tff(2906,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2907,plain,
% 1.86/2.03 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.03 inference(rewrite,[status(thm)],[])).
% 1.86/2.03 tff(2908,plain,
% 1.86/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2907])).
% 1.86/2.04 tff(2909,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2908, 2906])).
% 1.86/2.04 tff(2910,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2911,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 1.86/2.04 tff(2912,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2911, 106, 2905, 2895, 2890, 2886])).
% 1.86/2.04 tff(2913,plain,(r(elem!1, s(z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | b(s(s(s(s(z)))), s(s(z))) | b(s(z), elem!1) | b(elem!1, s(s(s(z)))) | b(z, elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2914,plain,
% 1.86/2.04 (r(elem!1, s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2913, 357, 126, 260, 259, 2671, 95, 554, 367, 1427, 946, 258, 84])).
% 1.86/2.04 tff(2915,plain,
% 1.86/2.04 (~r(z, elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1376, 2914, 94, 95])).
% 1.86/2.04 tff(2916,plain,
% 1.86/2.04 (z = elem!1),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[651, 2915, 258])).
% 1.86/2.04 tff(2917,plain,
% 1.86/2.04 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2916])).
% 1.86/2.04 tff(2918,plain,
% 1.86/2.04 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2917, 759])).
% 1.86/2.04 tff(2919,plain,
% 1.86/2.04 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2918])).
% 1.86/2.04 tff(2920,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[140, 2919])).
% 1.86/2.04 tff(2921,plain,
% 1.86/2.04 (s(elem!1) = s(z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[703, 2916])).
% 1.86/2.04 tff(2922,plain,
% 1.86/2.04 (~b(elem!1, s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[948, 2921, 946])).
% 1.86/2.04 tff(2923,plain,
% 1.86/2.04 (r(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[942, 2922, 2921])).
% 1.86/2.04 tff(2924,plain,
% 1.86/2.04 (~r(s(s(s(z))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1938, 2923, 554, 2914])).
% 1.86/2.04 tff(2925,plain,
% 1.86/2.04 (b(s(s(s(z))), s(z))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1173, 2924])).
% 1.86/2.04 tff(2926,plain,
% 1.86/2.04 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(transitivity,[status(thm)],[2918, 760])).
% 1.86/2.04 tff(2927,plain,
% 1.86/2.04 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2926])).
% 1.86/2.04 tff(2928,plain,
% 1.86/2.04 (~(s(s(s(s(s(z))))) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[140, 2927])).
% 1.86/2.04 tff(2929,plain,
% 1.86/2.04 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2916])).
% 1.86/2.04 tff(2930,plain,
% 1.86/2.04 (r(elem!1, s(s(s(z)))) <=> r(z, s(s(s(z))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[2929])).
% 1.86/2.04 tff(2931,plain,
% 1.86/2.04 (r(z, s(s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2923, 2930])).
% 1.86/2.04 tff(2932,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2021, 2931, 2928, 94, 2671, 259, 2921, 126, 260, 357, 2714, 83, 2925, 554, 2914, 2920, 95])).
% 1.86/2.04 tff(2933,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | b(elem!1, s(s(s(z)))) | b(z, elem!1) | b(s(s(s(s(z)))), s(s(z))) | b(s(z), elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2934,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2933, 1960, 126, 260, 83, 554, 95, 946, 258, 259, 1427, 84])).
% 1.86/2.04 tff(2935,plain,
% 1.86/2.04 (~b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[566, 2934, 259, 1960])).
% 1.86/2.04 tff(2936,plain,
% 1.86/2.04 (r(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[454, 2935, 254])).
% 1.86/2.04 tff(2937,plain,
% 1.86/2.04 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[463, 2936, 126, 260])).
% 1.86/2.04 tff(2938,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[225, 2937])).
% 1.86/2.04 tff(2939,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[587, 1960, 2669, 260, 259, 554])).
% 1.86/2.04 tff(2940,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[205, 2939])).
% 1.86/2.04 tff(2941,plain,
% 1.86/2.04 (~b(z, s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[669, 2934, 258, 95, 83, 2714, 1960, 126, 260, 259])).
% 1.86/2.04 tff(2942,plain,
% 1.86/2.04 (r(z, s(s(z)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[124, 2941])).
% 1.86/2.04 tff(2943,plain,
% 1.86/2.04 (~r(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2138, 2942, 95, 259, 2934, 94])).
% 1.86/2.04 tff(2944,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[274, 2943])).
% 1.86/2.04 tff(2945,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2946,plain,
% 1.86/2.04 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(2947,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2946])).
% 1.86/2.04 tff(2948,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2947, 2945])).
% 1.86/2.04 tff(2949,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(2950,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2949, 2948])).
% 1.86/2.04 tff(2951,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2950, 106, 554, 637, 95, 600])).
% 1.86/2.04 tff(2952,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2953,plain,
% 1.86/2.04 (~r(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2952, 2942, 554, 95])).
% 1.86/2.04 tff(2954,plain,
% 1.86/2.04 (b(s(s(z)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[157, 2953])).
% 1.86/2.04 tff(2955,plain,
% 1.86/2.04 (~(elem!1 = s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2331, 2954, 260, 126, 2934, 94, 2942, 2944, 259, 95, 2115, 1427, 258])).
% 1.86/2.04 tff(2956,plain,
% 1.86/2.04 (r(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2112, 2955])).
% 1.86/2.04 tff(2957,plain,
% 1.86/2.04 (~(z = elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2023, 2940, 259, 126, 260, 2714, 83, 554, 95, 2956, 84])).
% 1.86/2.04 tff(2958,plain,
% 1.86/2.04 (r(z, elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[651, 2957, 258])).
% 1.86/2.04 tff(2959,plain,
% 1.86/2.04 (~r(s(z), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1454, 2958, 95, 2956])).
% 1.86/2.04 tff(2960,plain,
% 1.86/2.04 (s(z) = elem!1),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1444, 2959, 1427])).
% 1.86/2.04 tff(2961,plain,
% 1.86/2.04 (s(s(z)) = s(elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2960])).
% 1.86/2.04 tff(2962,plain,
% 1.86/2.04 (s(s(s(z))) = s(s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2961])).
% 1.86/2.04 tff(2963,plain,
% 1.86/2.04 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2962])).
% 1.86/2.04 tff(2964,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2963])).
% 1.86/2.04 tff(2965,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[83, 2964])).
% 1.86/2.04 tff(2966,plain,
% 1.86/2.04 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2961])).
% 1.86/2.04 tff(2967,plain,
% 1.86/2.04 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.04 inference(symmetry,[status(thm)],[2966])).
% 1.86/2.04 tff(2968,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2963, 2961])).
% 1.86/2.04 tff(2969,plain,
% 1.86/2.04 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2968, 2967])).
% 1.86/2.04 tff(2970,plain,
% 1.86/2.04 (b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2934, 2969])).
% 1.86/2.04 tff(2971,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2018, 2970, 2965, 2940, 2938])).
% 1.86/2.04 tff(2972,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), elem!1) | (~r(s(z), z)) | b(z, elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, s(z)) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(2973,plain,
% 1.86/2.04 (b(elem!1, s(s(s(z))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2972, 2100, 83, 95, 258, 259, 126, 260, 84, 551])).
% 1.86/2.04 tff(2974,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2344])).
% 1.86/2.04 tff(2975,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.04 inference(symmetry,[status(thm)],[2974])).
% 1.86/2.04 tff(2976,plain,
% 1.86/2.04 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1435])).
% 1.86/2.04 tff(2977,plain,
% 1.86/2.04 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[2976, 1043])).
% 1.86/2.04 tff(2978,plain,
% 1.86/2.04 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.04 inference(transitivity,[status(thm)],[2977, 1044])).
% 1.86/2.04 tff(2979,plain,
% 1.86/2.04 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2978])).
% 1.86/2.04 tff(2980,plain,
% 1.86/2.04 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[726, 2979])).
% 1.86/2.04 tff(2981,plain,
% 1.86/2.04 (r(s(z), z) <=> r(elem!1, z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1435])).
% 1.86/2.04 tff(2982,plain,
% 1.86/2.04 (r(elem!1, z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[95, 2981])).
% 1.86/2.04 tff(2983,plain,
% 1.86/2.04 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2082])).
% 1.86/2.04 tff(2984,plain,
% 1.86/2.04 (b(s(elem!1), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2072, 2983])).
% 1.86/2.04 tff(2985,plain,
% 1.86/2.04 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2816, 2984, 1435, 1356, 2068, 2982])).
% 1.86/2.04 tff(2986,plain,
% 1.86/2.04 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1110, 2985, 2980])).
% 1.86/2.04 tff(2987,plain,
% 1.86/2.04 (b(s(s(s(s(s(z))))), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2986, 2975])).
% 1.86/2.04 tff(2988,plain,
% 1.86/2.04 (~b(s(s(s(z))), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2046, 2987, 1369, 2973])).
% 1.86/2.04 tff(2989,plain,
% 1.86/2.04 (~b(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2988, 2087])).
% 1.86/2.04 tff(2990,plain,
% 1.86/2.04 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.86/2.04 inference(commutativity,[status(thm)],[])).
% 1.86/2.04 tff(2991,plain,
% 1.86/2.04 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 1.86/2.04 inference(symmetry,[status(thm)],[2990])).
% 1.86/2.04 tff(2992,plain,
% 1.86/2.04 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2991])).
% 1.86/2.04 tff(2993,plain,
% 1.86/2.04 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2084])).
% 1.86/2.04 tff(2994,plain,
% 1.86/2.04 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 1.86/2.04 inference(transitivity,[status(thm)],[2993, 2101])).
% 1.86/2.04 tff(2995,plain,
% 1.86/2.04 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 1.86/2.04 inference(symmetry,[status(thm)],[2994])).
% 1.86/2.04 tff(2996,plain,
% 1.86/2.04 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(elem!1))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2995])).
% 1.86/2.04 tff(2997,plain,
% 1.86/2.04 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 1.86/2.04 inference(monotonicity,[status(thm)],[1435])).
% 1.86/2.04 tff(2998,plain,
% 1.86/2.04 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2997])).
% 1.86/2.04 tff(2999,plain,
% 1.86/2.04 (~(s(s(s(z))) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[344, 2998])).
% 1.86/2.04 tff(3000,plain,
% 1.86/2.04 (~(elem!1 = s(s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[2999, 2996])).
% 1.86/2.04 tff(3001,plain,
% 1.86/2.04 (~(s(s(elem!1)) = elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3000, 2992])).
% 1.86/2.04 tff(3002,plain,
% 1.86/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3003,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3004,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3003, 3002])).
% 1.86/2.04 tff(3005,plain,
% 1.86/2.04 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3004, 25])).
% 1.86/2.04 tff(3006,plain,
% 1.86/2.04 (r(s(s(elem!1)), elem!1)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3005, 3001, 2989])).
% 1.86/2.04 tff(3007,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3008,plain,
% 1.86/2.04 (((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3009,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[3008])).
% 1.86/2.04 tff(3010,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.86/2.04 inference(transitivity,[status(thm)],[3009, 3007])).
% 1.86/2.04 tff(3011,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3012,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3011, 3010])).
% 1.86/2.04 tff(3013,plain,
% 1.86/2.04 (~r(z, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3012, 106, 2068, 2982, 3006])).
% 1.86/2.04 tff(3014,plain,
% 1.86/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3015,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3016,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3015, 3014])).
% 1.86/2.04 tff(3017,plain,
% 1.86/2.04 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3016, 25, 3013])).
% 1.86/2.04 tff(3018,plain,
% 1.86/2.04 (b(z, s(s(elem!1)))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3017, 2081])).
% 1.86/2.04 tff(3019,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3020,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3021,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3020, 3019])).
% 1.86/2.04 tff(3022,plain,
% 1.86/2.04 (~r(s(s(elem!1)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3021, 106, 2068, 2982, 3006])).
% 1.86/2.04 tff(3023,plain,
% 1.86/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3024,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3025,plain,
% 1.86/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3024, 3023])).
% 1.86/2.04 tff(3026,plain,
% 1.86/2.04 (b(s(s(elem!1)), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3025, 25, 816, 3022])).
% 1.86/2.04 tff(3027,plain,
% 1.86/2.04 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[2360])).
% 1.86/2.04 tff(3028,plain,
% 1.86/2.04 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(elem!1))))),
% 1.86/2.04 inference(symmetry,[status(thm)],[3027])).
% 1.86/2.04 tff(3029,plain,
% 1.86/2.04 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[3028])).
% 1.86/2.04 tff(3030,plain,
% 1.86/2.04 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[448, 3029])).
% 1.86/2.04 tff(3031,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2209, 3030])).
% 1.86/2.04 tff(3032,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(3033,plain,
% 1.86/2.04 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3032, 2357, 611])).
% 1.86/2.04 tff(3034,plain,
% 1.86/2.04 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[2229, 3033])).
% 1.86/2.04 tff(3035,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.86/2.04 tff(3036,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3037,plain,
% 1.86/2.04 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.86/2.04 inference(rewrite,[status(thm)],[])).
% 1.86/2.04 tff(3038,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.86/2.04 inference(monotonicity,[status(thm)],[3037])).
% 1.86/2.04 tff(3039,plain,
% 1.86/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.86/2.04 inference(transitivity,[status(thm)],[3038, 3036])).
% 1.86/2.04 tff(3040,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.86/2.04 inference(quant_inst,[status(thm)],[])).
% 1.86/2.04 tff(3041,plain,
% 1.86/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3040, 3039])).
% 1.86/2.04 tff(3042,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3041, 106, 638, 2231, 95, 3035])).
% 1.86/2.04 tff(3043,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(3044,plain,
% 1.86/2.04 (~r(s(s(s(elem!1))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3043, 3034, 95, 2068])).
% 1.86/2.04 tff(3045,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.86/2.04 tff(3046,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.86/2.04 tff(3047,plain,
% 1.86/2.04 ($false),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[1578, 25, 724, 3046, 3045])).
% 1.86/2.04 tff(3048,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.04 tff(3049,plain,
% 1.86/2.04 (b(s(s(s(elem!1))), z)),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[3048, 3044])).
% 1.86/2.04 tff(3050,plain,
% 1.86/2.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[608, 2076, 95, 551])).
% 1.86/2.04 tff(3051,plain,
% 1.86/2.04 (b(s(s(z)), s(s(s(s(z)))))),
% 1.86/2.04 inference(unit_resolution,[status(thm)],[351, 3050])).
% 1.86/2.04 tff(3052,plain,
% 1.86/2.04 (b(s(elem!1), s(s(s(elem!1))))),
% 1.86/2.04 inference(modus_ponens,[status(thm)],[3051, 2351])).
% 1.86/2.04 tff(3053,plain,
% 1.86/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3054,plain,
% 1.86/2.05 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3055,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3054])).
% 1.86/2.05 tff(3056,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3055, 3053])).
% 1.86/2.05 tff(3057,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3058,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3057, 3056])).
% 1.86/2.05 tff(3059,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3058, 171, 3052, 2984, 3049, 3026, 3018])).
% 1.86/2.05 tff(3060,plain,((~(s(z) = elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | b(z, elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3061,plain,
% 1.86/2.05 (~(s(z) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3060, 260, 95, 258, 259, 126, 83, 84])).
% 1.86/2.05 tff(3062,plain,
% 1.86/2.05 (b(s(z), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1444, 1651, 1924])).
% 1.86/2.05 tff(3063,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3064,plain,
% 1.86/2.05 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3065,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3064])).
% 1.86/2.05 tff(3066,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3065, 3063])).
% 1.86/2.05 tff(3067,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3068,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3067, 3066])).
% 1.86/2.05 tff(3069,plain,
% 1.86/2.05 ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3068, 171])).
% 1.86/2.05 tff(3070,plain,
% 1.86/2.05 (~b(elem!1, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3069, 3062, 259, 666])).
% 1.86/2.05 tff(3071,plain,
% 1.86/2.05 (elem!1 = s(z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[687, 3070, 676])).
% 1.86/2.05 tff(3072,plain,
% 1.86/2.05 (s(z) = elem!1),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3071, 2154])).
% 1.86/2.05 tff(3073,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1651, 3072])).
% 1.86/2.05 tff(3074,plain,((s(z) = elem!1) | r(elem!1, s(z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)) | r(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3075,plain,
% 1.86/2.05 (r(s(z), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3074, 3061, 259, 1882, 2069])).
% 1.86/2.05 tff(3076,plain,
% 1.86/2.05 (~r(elem!1, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1454, 3075, 95, 2068])).
% 1.86/2.05 tff(3077,assumption,(elem!1 = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.05 tff(3078,plain,
% 1.86/2.05 (~(z = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[703, 701])).
% 1.86/2.05 tff(3079,plain,
% 1.86/2.05 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.05 tff(3080,plain,
% 1.86/2.05 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.05 tff(3081,plain,
% 1.86/2.05 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = elem!1)),
% 1.86/2.05 inference(symmetry,[status(thm)],[3080])).
% 1.86/2.05 tff(3082,plain,
% 1.86/2.05 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (elem!1 = s(s(s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3081, 2102])).
% 1.86/2.05 tff(3083,plain,
% 1.86/2.05 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3082])).
% 1.86/2.05 tff(3084,plain,
% 1.86/2.05 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.05 tff(3085,plain,
% 1.86/2.05 (s(s(s(s(s(s(z)))))) = s(elem!1)),
% 1.86/2.05 inference(symmetry,[status(thm)],[3084])).
% 1.86/2.05 tff(3086,plain,
% 1.86/2.05 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[407])).
% 1.86/2.05 tff(3087,plain,
% 1.86/2.05 (s(s(z)) = s(elem!1)),
% 1.86/2.05 inference(transitivity,[status(thm)],[341, 408, 48, 3086, 3085])).
% 1.86/2.05 tff(3088,plain,
% 1.86/2.05 ((elem!1 = s(z)) <=> (s(s(s(s(s(z))))) = s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.05 tff(3089,plain,
% 1.86/2.05 ((elem!1 = s(z)) <=> (s(z) = s(s(s(s(s(z))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3088, 33])).
% 1.86/2.05 tff(3090,plain,
% 1.86/2.05 ((s(z) = s(s(s(s(s(z)))))) <=> (elem!1 = s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3089])).
% 1.86/2.05 tff(3091,plain,
% 1.86/2.05 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(elem!1 = s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3090])).
% 1.86/2.05 tff(3092,plain,
% 1.86/2.05 (~(elem!1 = s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[55, 3091])).
% 1.86/2.05 tff(3093,plain,
% 1.86/2.05 (~(s(s(z)) = s(elem!1))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1551, 3092])).
% 1.86/2.05 tff(3094,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3093, 3087])).
% 1.86/2.05 tff(3095,plain,((~(s(s(s(z))) = s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3096,plain,
% 1.86/2.05 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3095, 3077])).
% 1.86/2.05 tff(3097,plain,
% 1.86/2.05 (~(elem!1 = s(s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3096, 3083])).
% 1.86/2.05 tff(3098,plain,
% 1.86/2.05 (b(elem!1, s(s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[940, 3097])).
% 1.86/2.05 tff(3099,plain,
% 1.86/2.05 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3098, 3079])).
% 1.86/2.05 tff(3100,plain,
% 1.86/2.05 (~(elem!1 = z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[697, 3078])).
% 1.86/2.05 tff(3101,plain,
% 1.86/2.05 (r(elem!1, s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.05 tff(3102,plain,
% 1.86/2.05 ((~r(elem!1, s(z))) <=> (~r(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3101])).
% 1.86/2.05 tff(3103,plain,
% 1.86/2.05 (~r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[676, 3102])).
% 1.86/2.05 tff(3104,plain,
% 1.86/2.05 (b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[479, 3103])).
% 1.86/2.05 tff(3105,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 1.86/2.05 tff(3106,plain,
% 1.86/2.05 (s(s(z)) = elem!1),
% 1.86/2.05 inference(symmetry,[status(thm)],[3105])).
% 1.86/2.05 tff(3107,plain,
% 1.86/2.05 (s(s(z)) = s(s(s(s(s(z)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3106, 3077])).
% 1.86/2.05 tff(3108,plain,
% 1.86/2.05 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3107])).
% 1.86/2.05 tff(3109,plain,
% 1.86/2.05 (s(z) = s(s(s(s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[71, 3108, 48])).
% 1.86/2.05 tff(3110,plain,
% 1.86/2.05 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3109])).
% 1.86/2.05 tff(3111,plain,
% 1.86/2.05 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3110])).
% 1.86/2.05 tff(3112,plain,
% 1.86/2.05 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3107])).
% 1.86/2.05 tff(3113,plain,
% 1.86/2.05 (s(s(s(s(s(s(z)))))) = s(s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3112])).
% 1.86/2.05 tff(3114,plain,
% 1.86/2.05 (s(s(s(s(s(s(z)))))) = z),
% 1.86/2.05 inference(transitivity,[status(thm)],[3113, 191, 3111, 44])).
% 1.86/2.05 tff(3115,plain,
% 1.86/2.05 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3116,plain,
% 1.86/2.05 (~(s(s(s(s(s(s(z)))))) = z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3115, 13])).
% 1.86/2.05 tff(3117,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3116, 3114])).
% 1.86/2.05 tff(3118,plain,((~(elem!1 = s(s(z)))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3119,plain,
% 1.86/2.05 (~(elem!1 = s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3118, 3077])).
% 1.86/2.05 tff(3120,plain,
% 1.86/2.05 ((s(s(z)) = elem!1) <=> (elem!1 = s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[1479])).
% 1.86/2.05 tff(3121,plain,
% 1.86/2.05 (elem!1 = s(s(z))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[1418, 3120])).
% 1.86/2.05 tff(3122,assumption,(~(elem!1 = s(s(z)))), introduced(assumption)).
% 1.86/2.05 tff(3123,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3122, 3121])).
% 1.86/2.05 tff(3124,plain,((~(s(s(z)) = elem!1)) | (elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3125,plain,
% 1.86/2.05 (~(s(s(z)) = elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3124, 3119])).
% 1.86/2.05 tff(3126,plain,
% 1.86/2.05 (b(s(s(z)), elem!1)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[1416, 3125, 1570])).
% 1.86/2.05 tff(3127,plain,
% 1.86/2.05 (b(elem!1, s(z))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[687, 3092, 676])).
% 1.86/2.05 tff(3128,plain,
% 1.86/2.05 (s(s(s(s(s(z))))) = elem!1),
% 1.86/2.05 inference(symmetry,[status(thm)],[3077])).
% 1.86/2.05 tff(3129,plain,
% 1.86/2.05 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.05 tff(3130,plain,
% 1.86/2.05 (b(elem!1, s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3129])).
% 1.86/2.05 tff(3131,plain,
% 1.86/2.05 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.05 tff(3132,plain,
% 1.86/2.05 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3131])).
% 1.86/2.05 tff(3133,assumption,(b(s(z), z)), introduced(assumption)).
% 1.86/2.05 tff(3134,plain,
% 1.86/2.05 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3129])).
% 1.86/2.05 tff(3135,plain,
% 1.86/2.05 (b(z, s(s(s(s(s(z)))))) <=> b(z, elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.05 tff(3136,plain,
% 1.86/2.05 (b(z, elem!1) <=> b(z, s(s(s(s(s(z))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3135])).
% 1.86/2.05 tff(3137,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.86/2.05 tff(3138,plain,
% 1.86/2.05 (b(z, s(s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3137, 3136])).
% 1.86/2.05 tff(3139,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.05 tff(3140,plain,
% 1.86/2.05 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3139])).
% 1.86/2.05 tff(3141,plain,
% 1.86/2.05 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[666, 3140])).
% 1.86/2.05 tff(3142,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3143,plain,
% 1.86/2.05 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(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))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3144,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3143])).
% 1.86/2.05 tff(3145,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3144, 3142])).
% 1.86/2.05 tff(3146,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3147,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3146, 3145])).
% 1.86/2.05 tff(3148,plain,
% 1.86/2.05 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3147, 171, 259, 3133, 4, 3141])).
% 1.86/2.05 tff(3149,plain,
% 1.86/2.05 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3148, 3138])).
% 1.86/2.05 tff(3150,plain,
% 1.86/2.05 (~b(elem!1, s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3149, 3134])).
% 1.86/2.05 tff(3151,plain,
% 1.86/2.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3152,plain,
% 1.86/2.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3153,plain,
% 1.86/2.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3152, 3151])).
% 1.86/2.05 tff(3154,plain,
% 1.86/2.05 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3153, 25])).
% 1.86/2.05 tff(3155,plain,
% 1.86/2.05 (r(elem!1, s(s(z)))),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3154, 3150, 3119])).
% 1.86/2.05 tff(3156,plain,
% 1.86/2.05 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3131])).
% 1.86/2.05 tff(3157,plain,
% 1.86/2.05 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3155, 3156])).
% 1.86/2.05 tff(3158,plain,
% 1.86/2.05 (r(z, s(s(s(s(s(z)))))) <=> r(z, elem!1)),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.05 tff(3159,plain,
% 1.86/2.05 (r(z, elem!1) <=> r(z, s(s(s(s(s(z))))))),
% 1.86/2.05 inference(symmetry,[status(thm)],[3158])).
% 1.86/2.05 tff(3160,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3161,plain,
% 1.86/2.05 (((~r(s(s(z)), z)) | (~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(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3162,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3161])).
% 1.86/2.05 tff(3163,plain,
% 1.86/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3162, 3160])).
% 1.86/2.05 tff(3164,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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))))))))),
% 1.86/2.05 inference(quant_inst,[status(thm)],[])).
% 1.86/2.05 tff(3165,plain,
% 1.86/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.05 inference(modus_ponens,[status(thm)],[3164, 3163])).
% 1.86/2.05 tff(3166,plain,
% 1.86/2.05 ($false),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3165, 106, 554, 637, 126, 396])).
% 1.86/2.05 tff(3167,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.05 tff(3168,plain,
% 1.86/2.05 (~r(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[3167, 396, 126, 554])).
% 1.86/2.05 tff(3169,plain,
% 1.86/2.05 (b(s(s(z)), z)),
% 1.86/2.05 inference(unit_resolution,[status(thm)],[157, 3168])).
% 1.86/2.05 tff(3170,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3171,plain,
% 1.86/2.05 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(rewrite,[status(thm)],[])).
% 1.86/2.05 tff(3172,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.05 inference(monotonicity,[status(thm)],[3171])).
% 1.86/2.05 tff(3173,plain,
% 1.86/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.05 inference(transitivity,[status(thm)],[3172, 3170])).
% 1.86/2.05 tff(3174,plain,
% 1.86/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3175,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3174, 3173])).
% 1.86/2.06 tff(3176,plain,
% 1.86/2.06 (~b(z, s(s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3175, 171, 1, 838, 1384, 160])).
% 1.86/2.06 tff(3177,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3176, 3138])).
% 1.86/2.06 tff(3178,plain,((~b(z, elem!1)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(3179,plain,
% 1.86/2.06 (~b(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3178, 3169, 3077, 838, 1384, 160])).
% 1.86/2.06 tff(3180,plain,
% 1.86/2.06 (r(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[651, 3179, 695])).
% 1.86/2.06 tff(3181,plain,
% 1.86/2.06 (r(z, s(s(s(s(s(z))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3180, 3159])).
% 1.86/2.06 tff(3182,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3183,plain,
% 1.86/2.06 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3184,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3183])).
% 1.86/2.06 tff(3185,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3184, 3182])).
% 1.86/2.06 tff(3186,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3187,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3186, 3185])).
% 1.86/2.06 tff(3188,plain,
% 1.86/2.06 ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3187, 106, 126, 396])).
% 1.86/2.06 tff(3189,plain,
% 1.86/2.06 (~r(s(z), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3188, 3181])).
% 1.86/2.06 tff(3190,plain,
% 1.86/2.06 (b(s(z), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[30, 3189])).
% 1.86/2.06 tff(3191,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3192,plain,
% 1.86/2.06 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3193,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3192])).
% 1.86/2.06 tff(3194,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3193, 3191])).
% 1.86/2.06 tff(3195,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3196,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3195, 3194])).
% 1.86/2.06 tff(3197,plain,
% 1.86/2.06 ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3196, 106, 126, 396])).
% 1.86/2.06 tff(3198,plain,
% 1.86/2.06 (~r(z, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3197, 3181])).
% 1.86/2.06 tff(3199,plain,
% 1.86/2.06 (b(z, s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[93, 3198])).
% 1.86/2.06 tff(3200,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3201,plain,
% 1.86/2.06 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3202,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3201])).
% 1.86/2.06 tff(3203,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3202, 3200])).
% 1.86/2.06 tff(3204,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3205,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3204, 3203])).
% 1.86/2.06 tff(3206,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3205, 171, 3199, 259, 3169, 3190])).
% 1.86/2.06 tff(3207,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (z = elem!1) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(3208,plain,
% 1.86/2.06 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3207, 3157, 126, 3077, 695, 3141, 1384, 259, 554])).
% 1.86/2.06 tff(3209,plain,
% 1.86/2.06 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[835, 3208, 3096])).
% 1.86/2.06 tff(3210,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[2463, 3156])).
% 1.86/2.06 tff(3211,plain,
% 1.86/2.06 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[2610, 106, 2604, 126, 1998])).
% 1.86/2.06 tff(3212,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3211, 3210])).
% 1.86/2.06 tff(3213,plain,((~r(elem!1, s(s(z)))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(3214,plain,
% 1.86/2.06 (~r(s(z), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3213, 3209, 3155, 126, 3077])).
% 1.86/2.06 tff(3215,plain,
% 1.86/2.06 (b(s(z), s(s(s(z))))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1996, 3214])).
% 1.86/2.06 tff(3216,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), z) <=> r(elem!1, z)),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.06 tff(3217,plain,
% 1.86/2.06 (r(elem!1, z) <=> r(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(symmetry,[status(thm)],[3216])).
% 1.86/2.06 tff(3218,plain,
% 1.86/2.06 (~(elem!1 = z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[697, 695])).
% 1.86/2.06 tff(3219,plain,
% 1.86/2.06 (~r(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3167, 3157, 126, 554])).
% 1.86/2.06 tff(3220,plain,
% 1.86/2.06 (b(s(s(z)), z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[157, 3219])).
% 1.86/2.06 tff(3221,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3222,plain,
% 1.86/2.06 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3223,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3222])).
% 1.86/2.06 tff(3224,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3223, 3221])).
% 1.86/2.06 tff(3225,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3226,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 1.86/2.06 tff(3227,plain,
% 1.86/2.06 ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3226, 171])).
% 1.86/2.06 tff(3228,plain,
% 1.86/2.06 (~b(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3227, 3220, 666, 3137])).
% 1.86/2.06 tff(3229,plain,
% 1.86/2.06 (r(elem!1, z)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1567, 3228, 3218])).
% 1.86/2.06 tff(3230,plain,
% 1.86/2.06 (r(s(s(s(s(s(z))))), z)),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3229, 3217])).
% 1.86/2.06 tff(3231,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3232,plain,
% 1.86/2.06 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3233,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3232])).
% 1.86/2.06 tff(3234,plain,
% 1.86/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3233, 3231])).
% 1.86/2.06 tff(3235,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3236,plain,
% 1.86/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3235, 3234])).
% 1.86/2.06 tff(3237,plain,
% 1.86/2.06 (~r(s(s(s(z))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3236, 106, 3209, 126, 3230])).
% 1.86/2.06 tff(3238,plain,
% 1.86/2.06 (b(s(s(s(z))), s(z))),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[1171, 25, 344, 3237])).
% 1.86/2.06 tff(3239,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3240,plain,
% 1.86/2.06 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.06 inference(rewrite,[status(thm)],[])).
% 1.86/2.06 tff(3241,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.06 inference(monotonicity,[status(thm)],[3240])).
% 1.86/2.06 tff(3242,plain,
% 1.86/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.06 inference(transitivity,[status(thm)],[3241, 3239])).
% 1.86/2.06 tff(3243,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.06 inference(quant_inst,[status(thm)],[])).
% 1.86/2.06 tff(3244,plain,
% 1.86/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[3243, 3242])).
% 1.86/2.06 tff(3245,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3244, 171, 3133, 3238, 3215, 1384, 4])).
% 1.86/2.06 tff(3246,plain,((~b(z, elem!1)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (z = elem!1) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.06 tff(3247,plain,
% 1.86/2.06 (~b(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[3246, 3133, 1384, 4, 126, 3077, 666, 3078, 259, 554])).
% 1.86/2.06 tff(3248,plain,
% 1.86/2.06 (r(z, elem!1)),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[651, 3247, 3078])).
% 1.86/2.06 tff(3249,plain,
% 1.86/2.06 (r(z, s(s(s(s(s(z))))))),
% 1.86/2.06 inference(modus_ponens,[status(thm)],[638, 3159])).
% 1.86/2.06 tff(3250,plain,
% 1.86/2.06 ($false),
% 1.86/2.06 inference(unit_resolution,[status(thm)],[493, 3249])).
% 1.86/2.07 tff(3251,plain,(r(z, s(s(s(s(s(z)))))) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3252,plain,
% 1.86/2.07 (r(z, s(s(s(s(s(z))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3251, 3248, 3077])).
% 1.86/2.07 tff(3253,plain,
% 1.86/2.07 (~r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3196, 106, 126, 396, 1288])).
% 1.86/2.07 tff(3254,plain,
% 1.86/2.07 (b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[93, 3253])).
% 1.86/2.07 tff(3255,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3205, 171, 3254, 259, 3169, 3133])).
% 1.86/2.07 tff(3256,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3257,plain,
% 1.86/2.07 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3256, 3133, 259, 126, 554, 3252])).
% 1.86/2.07 tff(3258,plain,
% 1.86/2.07 (~r(elem!1, s(s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3257, 3132])).
% 1.86/2.07 tff(3259,plain,
% 1.86/2.07 (b(elem!1, s(s(z)))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3154, 3258, 3119])).
% 1.86/2.07 tff(3260,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3259, 3130])).
% 1.86/2.07 tff(3261,plain,
% 1.86/2.07 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(z))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.07 tff(3262,plain,
% 1.86/2.07 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), elem!1)),
% 1.86/2.07 inference(symmetry,[status(thm)],[3261])).
% 1.86/2.07 tff(3263,plain,
% 1.86/2.07 (r(s(z), elem!1)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[126, 3262])).
% 1.86/2.07 tff(3264,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.07 tff(3265,plain,
% 1.86/2.07 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[3264])).
% 1.86/2.07 tff(3266,plain,
% 1.86/2.07 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3267,plain,
% 1.86/2.07 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3266, 42])).
% 1.86/2.07 tff(3268,plain,
% 1.86/2.07 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3269,plain,
% 1.86/2.07 (inj_0(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3268, 42])).
% 1.86/2.07 tff(3270,plain,
% 1.86/2.07 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3084])).
% 1.86/2.07 tff(3271,assumption,(s(s(s(s(s(z))))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.86/2.07 tff(3272,plain,
% 1.86/2.07 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3271])).
% 1.86/2.07 tff(3273,plain,
% 1.86/2.07 (s(s(s(s(z)))) = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[49, 3272, 812, 3270])).
% 1.86/2.07 tff(3274,plain,
% 1.86/2.07 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3273])).
% 1.86/2.07 tff(3275,plain,
% 1.86/2.07 (s(s(s(z))) = s(s(s(s(s(s(z))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[191, 3274, 3269])).
% 1.86/2.07 tff(3276,plain,
% 1.86/2.07 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3275])).
% 1.86/2.07 tff(3277,plain,
% 1.86/2.07 (s(s(z)) = elem!1),
% 1.86/2.07 inference(transitivity,[status(thm)],[341, 3276, 3267, 3128])).
% 1.86/2.07 tff(3278,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3125, 3277])).
% 1.86/2.07 tff(3279,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3280,plain,
% 1.86/2.07 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3279, 3077])).
% 1.86/2.07 tff(3281,assumption,(b(z, s(z))), introduced(assumption)).
% 1.86/2.07 tff(3282,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3283,plain,
% 1.86/2.07 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3284,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3283])).
% 1.86/2.07 tff(3285,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3284, 3282])).
% 1.86/2.07 tff(3286,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3287,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3286, 3285])).
% 1.86/2.07 tff(3288,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3287, 171, 3281, 259, 3133, 4, 207])).
% 1.86/2.07 tff(3289,plain,((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3290,plain,
% 1.86/2.07 (~b(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3289, 3133, 259, 4, 207])).
% 1.86/2.07 tff(3291,plain,
% 1.86/2.07 (r(z, s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[93, 3290])).
% 1.86/2.07 tff(3292,plain,
% 1.86/2.07 (~r(elem!1, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1660, 3291, 1446, 638])).
% 1.86/2.07 tff(3293,plain,
% 1.86/2.07 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3265])).
% 1.86/2.07 tff(3294,plain,
% 1.86/2.07 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[934, 3293])).
% 1.86/2.07 tff(3295,plain,
% 1.86/2.07 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.07 tff(3296,plain,
% 1.86/2.07 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[3295])).
% 1.86/2.07 tff(3297,plain,
% 1.86/2.07 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3296])).
% 1.86/2.07 tff(3298,plain,
% 1.86/2.07 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[2891, 3297])).
% 1.86/2.07 tff(3299,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) | r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1303, 25, 1300])).
% 1.86/2.07 tff(3300,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3299, 3298, 3294])).
% 1.86/2.07 tff(3301,plain,(r(elem!1, s(s(s(elem!1)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~(elem!1 = s(s(s(s(s(z))))))) | b(elem!1, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3302,plain,
% 1.86/2.07 (b(elem!1, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3301, 3292, 3077, 3280])).
% 1.86/2.07 tff(3303,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3302, 3265])).
% 1.86/2.07 tff(3304,plain,
% 1.86/2.07 (b(s(z), s(s(s(s(s(s(z))))))) <=> b(s(z), s(elem!1))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3085])).
% 1.86/2.07 tff(3305,plain,
% 1.86/2.07 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(symmetry,[status(thm)],[3304])).
% 1.86/2.07 tff(3306,plain,
% 1.86/2.07 (~r(elem!1, z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1562, 3291, 1446, 638])).
% 1.86/2.07 tff(3307,plain,
% 1.86/2.07 (b(elem!1, z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1567, 3306, 3100])).
% 1.86/2.07 tff(3308,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), z) <=> b(elem!1, z)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.07 tff(3309,plain,
% 1.86/2.07 (b(elem!1, z) <=> b(s(s(s(s(s(z))))), z)),
% 1.86/2.07 inference(symmetry,[status(thm)],[3308])).
% 1.86/2.07 tff(3310,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3307, 3309])).
% 1.86/2.07 tff(3311,plain,
% 1.86/2.07 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[944, 3265])).
% 1.86/2.07 tff(3312,plain,
% 1.86/2.07 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2217, 1809, 679, 259, 666])).
% 1.86/2.07 tff(3313,plain,
% 1.86/2.07 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[2227, 25, 3312, 2222])).
% 1.86/2.07 tff(3314,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3315,plain,
% 1.86/2.07 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3316,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3315])).
% 1.86/2.07 tff(3317,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3316, 3314])).
% 1.86/2.07 tff(3318,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3319,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 1.86/2.07 tff(3320,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3319, 106, 554, 991, 2231, 1769])).
% 1.86/2.07 tff(3321,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3322,plain,
% 1.86/2.07 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3321, 3313, 991, 554])).
% 1.86/2.07 tff(3323,plain,
% 1.86/2.07 ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1636, 25, 3322])).
% 1.86/2.07 tff(3324,plain,
% 1.86/2.07 (b(s(s(z)), s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3323, 1626])).
% 1.86/2.07 tff(3325,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3326,plain,
% 1.86/2.07 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3327,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3326])).
% 1.86/2.07 tff(3328,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3327, 3325])).
% 1.86/2.07 tff(3329,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3330,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 1.86/2.07 tff(3331,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3330, 171, 1809, 3133, 160, 2010, 159, 3324])).
% 1.86/2.07 tff(3332,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3333,plain,
% 1.86/2.07 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3332, 3133, 3141, 3311, 3310, 991, 554, 679, 259, 666])).
% 1.86/2.07 tff(3334,plain,
% 1.86/2.07 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1807, 3333])).
% 1.86/2.07 tff(3335,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3336,plain,
% 1.86/2.07 (((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3337,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3336])).
% 1.86/2.07 tff(3338,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3337, 3335])).
% 1.86/2.07 tff(3339,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3340,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3339, 3338])).
% 1.86/2.07 tff(3341,plain,
% 1.86/2.07 (~r(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3340, 106, 1571, 96, 1822])).
% 1.86/2.07 tff(3342,plain,
% 1.86/2.07 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1593, 25, 3341])).
% 1.86/2.07 tff(3343,plain,
% 1.86/2.07 (b(z, s(s(s(elem!1))))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3342, 1583])).
% 1.86/2.07 tff(3344,plain,
% 1.86/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3345,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3346,plain,
% 1.86/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3345, 3344])).
% 1.86/2.07 tff(3347,plain,
% 1.86/2.07 (~r(s(s(s(elem!1))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3346, 106, 1571, 96, 1822])).
% 1.86/2.07 tff(3348,plain,
% 1.86/2.07 (b(s(s(s(elem!1))), z)),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1578, 25, 724, 3347])).
% 1.86/2.07 tff(3349,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3350,plain,
% 1.86/2.07 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(rewrite,[status(thm)],[])).
% 1.86/2.07 tff(3351,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))))),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3350])).
% 1.86/2.07 tff(3352,plain,
% 1.86/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))))),
% 1.86/2.07 inference(transitivity,[status(thm)],[3351, 3349])).
% 1.86/2.07 tff(3353,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.86/2.07 inference(quant_inst,[status(thm)],[])).
% 1.86/2.07 tff(3354,plain,
% 1.86/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1)))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3353, 3352])).
% 1.86/2.07 tff(3355,plain,
% 1.86/2.07 ($false),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3354, 171, 1596, 944, 3348, 3343])).
% 1.86/2.07 tff(3356,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.07 tff(3357,plain,
% 1.86/2.07 (~r(s(z), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[3356, 3334, 944, 3291, 3307])).
% 1.86/2.07 tff(3358,plain,
% 1.86/2.07 (b(s(z), s(elem!1))),
% 1.86/2.07 inference(unit_resolution,[status(thm)],[1832, 3357, 1821])).
% 1.86/2.07 tff(3359,plain,
% 1.86/2.07 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.07 inference(modus_ponens,[status(thm)],[3358, 3305])).
% 1.86/2.07 tff(3360,plain,
% 1.86/2.07 (b(s(s(s(s(s(s(z)))))), z) <=> b(s(elem!1), z)),
% 1.86/2.07 inference(monotonicity,[status(thm)],[3085])).
% 1.86/2.07 tff(3361,plain,
% 1.86/2.07 (b(s(elem!1), z) <=> b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.07 inference(symmetry,[status(thm)],[3360])).
% 1.86/2.08 tff(3362,plain,
% 1.86/2.08 (~b(s(elem!1), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2728, 3358, 259, 679, 666])).
% 1.86/2.08 tff(3363,plain,
% 1.86/2.08 (r(s(elem!1), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1717, 3362, 701])).
% 1.86/2.08 tff(3364,plain,
% 1.86/2.08 (~r(s(elem!1), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1818, 3363, 554, 3291])).
% 1.86/2.08 tff(3365,plain,
% 1.86/2.08 (b(s(elem!1), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1691, 3364])).
% 1.86/2.08 tff(3366,plain,
% 1.86/2.08 (b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3365, 3361])).
% 1.86/2.08 tff(3367,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3368,plain,
% 1.86/2.08 (((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3369,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3368])).
% 1.86/2.08 tff(3370,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3369, 3367])).
% 1.86/2.08 tff(3371,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3372,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3371, 3370])).
% 1.86/2.08 tff(3373,plain,
% 1.86/2.08 ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3372, 171, 259, 4, 3141, 3310])).
% 1.86/2.08 tff(3374,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3373, 3366, 3359])).
% 1.86/2.08 tff(3375,plain,((~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3376,plain,
% 1.86/2.08 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3375, 3302, 4, 3077, 554, 701, 679, 666, 3133, 259, 1446, 638, 207])).
% 1.86/2.08 tff(3377,plain,
% 1.86/2.08 (b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1013, 3376])).
% 1.86/2.08 tff(3378,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2016, 171, 3377, 3141, 207, 3303])).
% 1.86/2.08 tff(3379,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3380,plain,
% 1.86/2.08 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3379, 3248, 3077, 4, 554, 701, 679, 666, 259, 3263, 3133])).
% 1.86/2.08 tff(3381,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3380, 3260])).
% 1.86/2.08 tff(3382,plain,((~b(s(z), z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3383,plain,
% 1.86/2.08 (~b(s(z), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3382, 3077, 259, 126, 554, 3104, 701, 3127, 3126, 3099])).
% 1.86/2.08 tff(3384,plain,
% 1.86/2.08 (r(s(z), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[30, 3383])).
% 1.86/2.08 tff(3385,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.86/2.08 tff(3386,plain,
% 1.86/2.08 (~b(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3227, 1, 666, 3137])).
% 1.86/2.08 tff(3387,plain,
% 1.86/2.08 (r(elem!1, z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1567, 3386, 3385])).
% 1.86/2.08 tff(3388,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), z)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3387, 3217])).
% 1.86/2.08 tff(3389,plain,
% 1.86/2.08 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3178, 1, 3141, 3137, 1384, 3077])).
% 1.86/2.08 tff(3390,plain,
% 1.86/2.08 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[835, 3389, 3096])).
% 1.86/2.08 tff(3391,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3392,plain,
% 1.86/2.08 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3393,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3392])).
% 1.86/2.08 tff(3394,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3393, 3391])).
% 1.86/2.08 tff(3395,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3396,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3395, 3394])).
% 1.86/2.08 tff(3397,plain,
% 1.86/2.08 (~r(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3396, 106, 3390, 126, 3388])).
% 1.86/2.08 tff(3398,plain,
% 1.86/2.08 (b(s(z), s(s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1996, 3397])).
% 1.86/2.08 tff(3399,plain,
% 1.86/2.08 (~r(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3236, 106, 3390, 126, 3388])).
% 1.86/2.08 tff(3400,plain,
% 1.86/2.08 (b(s(s(s(z))), s(z))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1171, 25, 344, 3399])).
% 1.86/2.08 tff(3401,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3402,plain,
% 1.86/2.08 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3403,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3402])).
% 1.86/2.08 tff(3404,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3403, 3401])).
% 1.86/2.08 tff(3405,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3406,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3405, 3404])).
% 1.86/2.08 tff(3407,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3406, 171, 3400, 3398, 1384, 4])).
% 1.86/2.08 tff(3408,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (elem!1 = z) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3409,plain,
% 1.86/2.08 (~b(s(s(z)), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3408, 3137, 4, 126, 3077, 3385, 666, 1384])).
% 1.86/2.08 tff(3410,plain,
% 1.86/2.08 (r(s(s(z)), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[157, 3409])).
% 1.86/2.08 tff(3411,plain,
% 1.86/2.08 (~r(z, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[2952, 3410, 95, 554])).
% 1.86/2.08 tff(3412,plain,
% 1.86/2.08 (b(z, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[124, 3411])).
% 1.86/2.08 tff(3413,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3414,plain,
% 1.86/2.08 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3415,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3414])).
% 1.86/2.08 tff(3416,plain,
% 1.86/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3415, 3413])).
% 1.86/2.08 tff(3417,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3418,plain,
% 1.86/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3417, 3416])).
% 1.86/2.08 tff(3419,plain,
% 1.86/2.08 ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3418, 171])).
% 1.86/2.08 tff(3420,plain,
% 1.86/2.08 (~b(elem!1, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3419, 3412, 666, 3137])).
% 1.86/2.08 tff(3421,plain,
% 1.86/2.08 (r(elem!1, s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3154, 3420, 3119])).
% 1.86/2.08 tff(3422,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3421, 3156])).
% 1.86/2.08 tff(3423,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3167, 3410, 126, 554])).
% 1.86/2.08 tff(3424,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3423, 3422])).
% 1.86/2.08 tff(3425,plain,((~b(z, elem!1)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = z) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3426,plain,
% 1.86/2.08 (~b(z, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3425, 3077, 3126, 126, 554, 3384, 3104, 3100, 3099])).
% 1.86/2.08 tff(3427,plain,
% 1.86/2.08 (r(z, elem!1)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[651, 3426, 3078])).
% 1.86/2.08 tff(3428,plain,
% 1.86/2.08 (r(z, s(s(s(s(s(z))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3251, 3427, 3077])).
% 1.86/2.08 tff(3429,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[1296, 3428, 126, 3384])).
% 1.86/2.08 tff(3430,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3431,plain,
% 1.86/2.08 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(rewrite,[status(thm)],[])).
% 1.86/2.08 tff(3432,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.86/2.08 inference(monotonicity,[status(thm)],[3431])).
% 1.86/2.08 tff(3433,plain,
% 1.86/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(transitivity,[status(thm)],[3432, 3430])).
% 1.86/2.08 tff(3434,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.86/2.08 inference(quant_inst,[status(thm)],[])).
% 1.86/2.08 tff(3435,plain,
% 1.86/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[3434, 3433])).
% 1.86/2.08 tff(3436,plain,
% 1.86/2.08 ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3435, 106, 95, 126])).
% 1.86/2.08 tff(3437,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3436, 3249, 127])).
% 1.86/2.08 tff(3438,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.08 tff(3439,plain,
% 1.86/2.08 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[3438, 3427, 126, 3384, 3077])).
% 1.86/2.08 tff(3440,plain,
% 1.86/2.08 (r(s(s(s(s(s(z))))), z)),
% 1.86/2.08 inference(modus_ponens,[status(thm)],[1554, 3217])).
% 1.86/2.08 tff(3441,plain,
% 1.86/2.08 ($false),
% 1.86/2.08 inference(unit_resolution,[status(thm)],[137, 3440])).
% 1.86/2.08 tff(3442,plain,((~r(elem!1, z)) | r(s(s(s(s(s(z))))), z) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3443,plain,
% 1.86/2.09 (~r(elem!1, z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3442, 3439, 3077])).
% 1.86/2.09 tff(3444,plain,
% 1.86/2.09 (b(elem!1, z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1567, 3443, 3100])).
% 1.86/2.09 tff(3445,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3444, 3309])).
% 1.86/2.09 tff(3446,plain,
% 1.86/2.09 (b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3126, 3140])).
% 1.86/2.09 tff(3447,plain,
% 1.86/2.09 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3167, 637, 126, 554])).
% 1.86/2.09 tff(3448,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[219, 3210])).
% 1.86/2.09 tff(3449,plain,((~r(elem!1, s(s(z)))) | r(s(s(s(s(s(z))))), s(s(z))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3450,plain,
% 1.86/2.09 (~r(elem!1, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3449, 3447, 3077])).
% 1.86/2.09 tff(3451,plain,
% 1.86/2.09 (b(elem!1, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3154, 3450, 3119])).
% 1.86/2.09 tff(3452,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3451, 3130])).
% 1.86/2.09 tff(3453,plain,
% 1.86/2.09 ((~r(s(s(s(s(s(z))))), z)) <=> (~r(elem!1, z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3216])).
% 1.86/2.09 tff(3454,plain,
% 1.86/2.09 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3438, 95, 126, 638, 3077])).
% 1.86/2.09 tff(3455,plain,
% 1.86/2.09 (~r(elem!1, z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 1.86/2.09 tff(3456,plain,
% 1.86/2.09 (b(elem!1, z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1567, 3455, 3385])).
% 1.86/2.09 tff(3457,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3456, 3309])).
% 1.86/2.09 tff(3458,plain,
% 1.86/2.09 (~r(z, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2952, 95, 637, 554])).
% 1.86/2.09 tff(3459,plain,
% 1.86/2.09 (b(z, s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[124, 3458])).
% 1.86/2.09 tff(3460,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3461,plain,
% 1.86/2.09 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(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(z, 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(z))))), z)))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3462,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), z))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3461])).
% 1.86/2.09 tff(3463,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), z)))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3462, 3460])).
% 1.86/2.09 tff(3464,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(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)))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3465,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3464, 3463])).
% 1.86/2.09 tff(3466,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3465, 171, 3459, 160, 207, 3457])).
% 1.86/2.09 tff(3467,plain,((~r(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~(elem!1 = s(s(s(s(s(z))))))) | (elem!1 = z) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3468,plain,
% 1.86/2.09 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3467, 637, 95, 638, 554, 3077, 3385, 126, 160])).
% 1.86/2.09 tff(3469,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3468, 3452])).
% 1.86/2.09 tff(3470,plain,((~r(s(s(z)), z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (elem!1 = z) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3471,plain,
% 1.86/2.09 (~r(s(s(z)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3470, 3077, 3384, 3427, 554, 3100, 126, 3446])).
% 1.86/2.09 tff(3472,plain,
% 1.86/2.09 (b(s(s(z)), z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[157, 3471])).
% 1.86/2.09 tff(3473,assumption,(s(s(z)) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.09 tff(3474,plain,
% 1.86/2.09 (s(s(z)) = s(elem!1)),
% 1.86/2.09 inference(transitivity,[status(thm)],[3473, 3085])).
% 1.86/2.09 tff(3475,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3093, 3474])).
% 1.86/2.09 tff(3476,plain,((~(s(s(z)) = s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3477,plain,
% 1.86/2.09 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3476, 3077])).
% 1.86/2.09 tff(3478,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))) <=> b(s(elem!1), elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3085, 3128])).
% 1.86/2.09 tff(3479,plain,
% 1.86/2.09 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3478])).
% 1.86/2.09 tff(3480,plain,
% 1.86/2.09 ((s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))) <=> (s(elem!1) = elem!1)),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3085, 3128])).
% 1.86/2.09 tff(3481,plain,
% 1.86/2.09 ((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) <=> (~(s(elem!1) = elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3480])).
% 1.86/2.09 tff(3482,assumption,(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))), introduced(assumption)).
% 1.86/2.09 tff(3483,plain,
% 1.86/2.09 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3482])).
% 1.86/2.09 tff(3484,plain,
% 1.86/2.09 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3483])).
% 1.86/2.09 tff(3485,plain,
% 1.86/2.09 (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3482])).
% 1.86/2.09 tff(3486,plain,
% 1.86/2.09 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3077, 3485, 3484])).
% 1.86/2.09 tff(3487,assumption,(~(elem!1 = s(s(s(s(s(s(s(z))))))))), introduced(assumption)).
% 1.86/2.09 tff(3488,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3487, 3486])).
% 1.86/2.09 tff(3489,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3490,plain,
% 1.86/2.09 (elem!1 = s(s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3489, 3482, 3077])).
% 1.86/2.09 tff(3491,plain,
% 1.86/2.09 (s(s(s(s(s(s(s(z))))))) = s(s(elem!1))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3270])).
% 1.86/2.09 tff(3492,plain,
% 1.86/2.09 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3077, 3491])).
% 1.86/2.09 tff(3493,plain,
% 1.86/2.09 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(z))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3492, 881])).
% 1.86/2.09 tff(3494,plain,
% 1.86/2.09 ((elem!1 = s(s(s(s(s(s(s(z)))))))) <=> (s(s(s(s(s(z))))) = s(s(elem!1)))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3493, 882])).
% 1.86/2.09 tff(3495,assumption,(elem!1 = s(s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.09 tff(3496,plain,
% 1.86/2.09 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 1.86/2.09 tff(3497,assumption,(~(s(s(s(s(s(z))))) = s(s(elem!1)))), introduced(assumption)).
% 1.86/2.09 tff(3498,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3497, 3496])).
% 1.86/2.09 tff(3499,plain,((~(elem!1 = s(s(s(s(s(s(s(z))))))))) | (s(s(s(s(s(z))))) = s(s(elem!1))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3500,plain,
% 1.86/2.09 (s(s(s(s(s(z))))) = s(s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3499, 3490, 3077])).
% 1.86/2.09 tff(3501,assumption,(s(s(s(s(s(z))))) = s(s(elem!1))), introduced(assumption)).
% 1.86/2.09 tff(3502,plain,
% 1.86/2.09 (s(s(elem!1)) = s(s(s(s(s(z)))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3501])).
% 1.86/2.09 tff(3503,plain,
% 1.86/2.09 (s(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3491, 3502])).
% 1.86/2.09 tff(3504,plain,
% 1.86/2.09 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(s(s(s(z))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3503])).
% 1.86/2.09 tff(3505,plain,
% 1.86/2.09 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3270])).
% 1.86/2.09 tff(3506,plain,
% 1.86/2.09 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.09 inference(transitivity,[status(thm)],[3505, 3504, 3085])).
% 1.86/2.09 tff(3507,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1618, 3506])).
% 1.86/2.09 tff(3508,plain,((~(s(s(s(s(s(z))))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3509,plain,
% 1.86/2.09 (s(s(s(elem!1))) = s(elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3508, 3500, 3077])).
% 1.86/2.09 tff(3510,plain,
% 1.86/2.09 (s(s(s(elem!1))) = elem!1),
% 1.86/2.09 inference(transitivity,[status(thm)],[3509, 3084, 3482, 3128])).
% 1.86/2.09 tff(3511,plain,
% 1.86/2.09 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.09 inference(commutativity,[status(thm)],[])).
% 1.86/2.09 tff(3512,plain,
% 1.86/2.09 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3128])).
% 1.86/2.09 tff(3513,plain,
% 1.86/2.09 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.86/2.09 inference(transitivity,[status(thm)],[3512, 3511])).
% 1.86/2.09 tff(3514,plain,
% 1.86/2.09 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3513])).
% 1.86/2.09 tff(3515,plain,
% 1.86/2.09 (~(s(s(s(elem!1))) = elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3280, 3514])).
% 1.86/2.09 tff(3516,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3515, 3510])).
% 1.86/2.09 tff(3517,plain,((~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3518,plain,
% 1.86/2.09 (~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3517, 3077])).
% 1.86/2.09 tff(3519,plain,
% 1.86/2.09 (~(s(elem!1) = elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3518, 3481])).
% 1.86/2.09 tff(3520,plain,
% 1.86/2.09 (~r(elem!1, z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1562, 96, 1446, 638])).
% 1.86/2.09 tff(3521,plain,
% 1.86/2.09 (b(elem!1, z)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1567, 3520, 3100])).
% 1.86/2.09 tff(3522,plain,
% 1.86/2.09 ((s(z) = s(s(s(s(s(z)))))) <=> (s(z) = elem!1)),
% 1.86/2.09 inference(transitivity,[status(thm)],[3090, 2154])).
% 1.86/2.09 tff(3523,plain,
% 1.86/2.09 ((~(s(z) = s(s(s(s(s(z))))))) <=> (~(s(z) = elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3522])).
% 1.86/2.09 tff(3524,plain,
% 1.86/2.09 (~(s(z) = elem!1)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[55, 3523])).
% 1.86/2.09 tff(3525,plain,
% 1.86/2.09 (~r(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1801, 3521, 679, 1, 3093, 259, 701, 96, 95, 638, 3524, 1570])).
% 1.86/2.09 tff(3526,plain,
% 1.86/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1807, 3525])).
% 1.86/2.09 tff(3527,plain,
% 1.86/2.09 (~b(s(z), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2217, 3526, 679, 259, 3126])).
% 1.86/2.09 tff(3528,plain,
% 1.86/2.09 (r(s(z), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2229, 3527])).
% 1.86/2.09 tff(3529,plain,
% 1.86/2.09 (~r(s(elem!1), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2255, 3528, 3126, 3521, 1, 96])).
% 1.86/2.09 tff(3530,plain,
% 1.86/2.09 (b(s(elem!1), s(z))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1717, 3529, 701])).
% 1.86/2.09 tff(3531,plain,
% 1.86/2.09 (~b(s(z), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[2728, 3530, 259, 679, 3126])).
% 1.86/2.09 tff(3532,plain,
% 1.86/2.09 (r(s(z), s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1861, 3531, 1821])).
% 1.86/2.09 tff(3533,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3521, 3309])).
% 1.86/2.09 tff(3534,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(elem!1), s(z))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3085])).
% 1.86/2.09 tff(3535,plain,
% 1.86/2.09 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3534])).
% 1.86/2.09 tff(3536,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(z))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3530, 3535])).
% 1.86/2.09 tff(3537,plain,
% 1.86/2.09 (b(z, s(s(s(s(s(s(z))))))) <=> b(z, s(elem!1))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3085])).
% 1.86/2.09 tff(3538,plain,
% 1.86/2.09 (b(z, s(elem!1)) <=> b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(symmetry,[status(thm)],[3537])).
% 1.86/2.09 tff(3539,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.86/2.09 tff(3540,plain,
% 1.86/2.09 (b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3539, 3538])).
% 1.86/2.09 tff(3541,assumption,(b(s(s(s(s(s(s(z)))))), s(z))), introduced(assumption)).
% 1.86/2.09 tff(3542,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3543,plain,
% 1.86/2.09 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(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(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3544,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3543])).
% 1.86/2.09 tff(3545,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3544, 3542])).
% 1.86/2.09 tff(3546,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3547,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3546, 3545])).
% 1.86/2.09 tff(3548,plain,
% 1.86/2.09 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3547, 171, 259, 1, 207, 159, 3541])).
% 1.86/2.09 tff(3549,plain,
% 1.86/2.09 ($false),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3548, 3540])).
% 1.86/2.09 tff(3550,plain,((~b(z, s(elem!1))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.09 tff(3551,plain,
% 1.86/2.09 (~b(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3550, 3536, 259, 1, 207, 3533, 3077])).
% 1.86/2.09 tff(3552,plain,
% 1.86/2.09 (r(z, s(elem!1))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1679, 3551])).
% 1.86/2.09 tff(3553,plain,
% 1.86/2.09 (~r(s(elem!1), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1869, 3552, 95, 3532])).
% 1.86/2.09 tff(3554,plain,
% 1.86/2.09 (b(s(elem!1), elem!1)),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1523, 3553, 3519])).
% 1.86/2.09 tff(3555,plain,
% 1.86/2.09 (b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3554, 3479])).
% 1.86/2.09 tff(3556,plain,
% 1.86/2.09 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[1303, 25, 3280, 1298])).
% 1.86/2.09 tff(3557,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3558,plain,
% 1.86/2.09 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(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(z))))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3559,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(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(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3558])).
% 1.86/2.09 tff(3560,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(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(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.09 inference(transitivity,[status(thm)],[3559, 3557])).
% 1.86/2.09 tff(3561,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(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(z)))))))))),
% 1.86/2.09 inference(quant_inst,[status(thm)],[])).
% 1.86/2.09 tff(3562,plain,
% 1.86/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.09 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 1.86/2.09 tff(3563,plain,
% 1.86/2.09 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.09 inference(unit_resolution,[status(thm)],[3562, 171, 3526, 3446, 3556, 3536, 3555])).
% 1.86/2.09 tff(3564,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3565,plain,
% 1.86/2.09 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(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(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.09 inference(rewrite,[status(thm)],[])).
% 1.86/2.09 tff(3566,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.09 inference(monotonicity,[status(thm)],[3565])).
% 1.86/2.09 tff(3567,plain,
% 1.86/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3566, 3564])).
% 1.86/2.10 tff(3568,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3569,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(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(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3568, 3567])).
% 1.86/2.10 tff(3570,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3569, 171, 3526, 4, 3446, 207, 3556])).
% 1.86/2.10 tff(3571,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1013, 3570])).
% 1.86/2.10 tff(3572,assumption,(r(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.10 tff(3573,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3574,plain,
% 1.86/2.10 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3575,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3574])).
% 1.86/2.10 tff(3576,plain,
% 1.86/2.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3575, 3573])).
% 1.86/2.10 tff(3577,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3578,plain,
% 1.86/2.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3577, 3576])).
% 1.86/2.10 tff(3579,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3578, 106, 554, 991, 2231, 3572])).
% 1.86/2.10 tff(3580,plain,((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3581,plain,
% 1.86/2.10 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3580, 3571, 3528, 554])).
% 1.86/2.10 tff(3582,plain,
% 1.86/2.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3583,plain,
% 1.86/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3584,plain,
% 1.86/2.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3583, 3582])).
% 1.86/2.10 tff(3585,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3584, 25, 3581, 3477, 3563])).
% 1.86/2.10 tff(3586,plain,((~r(z, s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | r(s(s(z)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3587,plain,
% 1.86/2.10 (~r(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3586, 207, 95, 554, 259, 1, 3077, 4, 1298, 679, 701, 638, 1570, 1446])).
% 1.86/2.10 tff(3588,plain,
% 1.86/2.10 (b(z, s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[93, 3587])).
% 1.86/2.10 tff(3589,assumption,(b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.10 tff(3590,plain,
% 1.86/2.10 ((~b(z, s(s(s(s(s(s(z)))))))) <=> (~b(z, s(elem!1)))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3537])).
% 1.86/2.10 tff(3591,plain,
% 1.86/2.10 (~r(s(elem!1), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1827, 1822, 95, 638])).
% 1.86/2.10 tff(3592,plain,
% 1.86/2.10 (b(s(elem!1), z)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1691, 3591])).
% 1.86/2.10 tff(3593,plain,
% 1.86/2.10 (b(s(s(s(s(s(s(z)))))), z)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3592, 3361])).
% 1.86/2.10 tff(3594,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3595,plain,
% 1.86/2.10 (((~b(z, s(z))) | (~b(z, 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(z)), z))) <=> ((~b(z, 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)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3596,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3595])).
% 1.86/2.10 tff(3597,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3596, 3594])).
% 1.86/2.10 tff(3598,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3599,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 1.86/2.10 tff(3600,plain,
% 1.86/2.10 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3599, 171, 3281, 1, 3589])).
% 1.86/2.10 tff(3601,plain,
% 1.86/2.10 (~b(z, s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3600, 3593])).
% 1.86/2.10 tff(3602,plain,
% 1.86/2.10 (~b(z, s(elem!1))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3601, 3590])).
% 1.86/2.10 tff(3603,plain,
% 1.86/2.10 (r(z, s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1679, 3602])).
% 1.86/2.10 tff(3604,plain,
% 1.86/2.10 ((~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) <=> (~b(s(elem!1), elem!1))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3478])).
% 1.86/2.10 tff(3605,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3606,plain,
% 1.86/2.10 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), 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(z)), 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3607,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3606])).
% 1.86/2.10 tff(3608,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3607, 3605])).
% 1.86/2.10 tff(3609,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(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(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3610,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3609, 3608])).
% 1.86/2.10 tff(3611,plain,
% 1.86/2.10 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3610, 171, 1, 160, 207, 3589])).
% 1.86/2.10 tff(3612,plain,
% 1.86/2.10 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3611, 3593])).
% 1.86/2.10 tff(3613,plain,
% 1.86/2.10 (~b(s(elem!1), elem!1)),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3612, 3604])).
% 1.86/2.10 tff(3614,plain,
% 1.86/2.10 (r(s(elem!1), elem!1)),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1523, 3613, 3519])).
% 1.86/2.10 tff(3615,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1869, 3614, 3603, 95, 1822])).
% 1.86/2.10 tff(3616,plain,((~r(s(z), s(elem!1))) | (~r(s(z), z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(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(z, s(z))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3617,plain,
% 1.86/2.10 (~r(s(z), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3616, 3589, 3077, 1, 160, 207, 95, 3281, 638])).
% 1.86/2.10 tff(3618,plain,
% 1.86/2.10 (b(s(z), s(elem!1))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1832, 3617, 1858])).
% 1.86/2.10 tff(3619,plain,
% 1.86/2.10 (b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3618, 3305])).
% 1.86/2.10 tff(3620,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3621,plain,
% 1.86/2.10 (((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, 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(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(rewrite,[status(thm)],[])).
% 1.86/2.10 tff(3622,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.10 inference(monotonicity,[status(thm)],[3621])).
% 1.86/2.10 tff(3623,plain,
% 1.86/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.10 inference(transitivity,[status(thm)],[3622, 3620])).
% 1.86/2.10 tff(3624,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.10 inference(quant_inst,[status(thm)],[])).
% 1.86/2.10 tff(3625,plain,
% 1.86/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.10 inference(modus_ponens,[status(thm)],[3624, 3623])).
% 1.86/2.10 tff(3626,plain,
% 1.86/2.10 (~b(s(z), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3625, 171, 3281, 1, 207, 159, 3589])).
% 1.86/2.10 tff(3627,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3626, 3619])).
% 1.86/2.10 tff(3628,plain,((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (s(z) = s(elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3629,plain,
% 1.86/2.10 (~b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3628, 3588, 3077, 1, 207, 159, 1821, 3446, 95, 638])).
% 1.86/2.10 tff(3630,assumption,(~b(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.10 tff(3631,assumption,(~(s(s(z)) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.10 tff(3632,assumption,(~r(s(s(z)), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 1.86/2.10 tff(3633,plain,
% 1.86/2.10 ($false),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3584, 25, 3632, 3631, 3630])).
% 1.86/2.10 tff(3634,plain,(b(s(s(z)), s(s(s(s(s(s(z))))))) | r(s(s(z)), s(s(s(s(s(s(z))))))) | (s(s(z)) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.10 tff(3635,plain,
% 1.86/2.10 (r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3634, 3629, 3477])).
% 1.86/2.10 tff(3636,plain,
% 1.86/2.10 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1305, 3280, 1298])).
% 1.86/2.10 tff(3637,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2018, 207, 3636, 3446])).
% 1.86/2.10 tff(3638,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), s(s(z)))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1013, 3637])).
% 1.86/2.10 tff(3639,plain,
% 1.86/2.10 (~r(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[3580, 3635, 3638, 554])).
% 1.86/2.10 tff(3640,plain,
% 1.86/2.10 (b(s(z), s(s(s(elem!1))))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2229, 3639])).
% 1.86/2.10 tff(3641,plain,
% 1.86/2.10 (~b(s(s(s(elem!1))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[2217, 3640, 679, 259, 3126])).
% 1.86/2.10 tff(3642,plain,
% 1.86/2.10 (r(s(s(s(elem!1))), s(z))),
% 1.86/2.10 inference(unit_resolution,[status(thm)],[1807, 3641])).
% 1.86/2.11 tff(3643,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3644,plain,
% 1.86/2.11 (((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3645,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3644])).
% 1.86/2.11 tff(3646,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3645, 3643])).
% 1.86/2.11 tff(3647,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(z)))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3648,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3647, 3646])).
% 1.86/2.11 tff(3649,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3648, 106, 554, 3642, 3638, 3635])).
% 1.86/2.11 tff(3650,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | r(s(s(s(s(s(z))))), s(s(s(elem!1)))) | (s(elem!1) = s(z)) | r(s(s(z)), elem!1) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3651,plain,
% 1.86/2.11 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3650, 3127, 554, 259, 3077, 3472, 3445, 3384, 3427, 3104, 3429, 701, 1570, 3263])).
% 1.86/2.11 tff(3652,plain,
% 1.86/2.11 (~b(elem!1, s(s(z)))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3651, 3134])).
% 1.86/2.11 tff(3653,plain,
% 1.86/2.11 (r(elem!1, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3154, 3652, 3119])).
% 1.86/2.11 tff(3654,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3449, 3653, 3077])).
% 1.86/2.11 tff(3655,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3187, 106, 3384, 126, 3654, 3428])).
% 1.86/2.11 tff(3656,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (s(elem!1) = s(z)) | r(s(s(z)), elem!1) | r(elem!1, s(s(s(z)))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3657,plain,
% 1.86/2.11 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3656, 3076, 126, 259, 2077, 551, 2070, 2069])).
% 1.86/2.11 tff(3658,plain,
% 1.86/2.11 (r(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[782, 3657, 1891])).
% 1.86/2.11 tff(3659,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3660,plain,
% 1.86/2.11 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3661,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3660])).
% 1.86/2.11 tff(3662,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3661, 3659])).
% 1.86/2.11 tff(3663,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3664,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 1.86/2.11 tff(3665,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3664, 106, 2068, 95, 3075, 3658])).
% 1.86/2.11 tff(3666,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | b(z, elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3667,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3666, 259, 61, 31, 258, 83, 84])).
% 1.86/2.11 tff(3668,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) | r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1156, 415])).
% 1.86/2.11 tff(3669,plain,
% 1.86/2.11 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3668, 3667])).
% 1.86/2.11 tff(3670,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1398, 1465, 31, 61])).
% 1.86/2.11 tff(3671,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[145, 3670])).
% 1.86/2.11 tff(3672,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[872, 171, 323, 259, 4, 160])).
% 1.86/2.11 tff(3673,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3674,plain,
% 1.86/2.11 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3673, 160, 323, 259])).
% 1.86/2.11 tff(3675,plain,
% 1.86/2.11 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[479, 3674])).
% 1.86/2.11 tff(3676,plain,
% 1.86/2.11 (~r(z, s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[486, 106, 96, 95, 3675])).
% 1.86/2.11 tff(3677,plain,
% 1.86/2.11 (b(z, s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[498, 3676])).
% 1.86/2.11 tff(3678,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3679,plain,
% 1.86/2.11 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(s(z))))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3680,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3679])).
% 1.86/2.11 tff(3681,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(s(z))))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3680, 3678])).
% 1.86/2.11 tff(3682,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(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(s(z))))))) | (~b(z, s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3683,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3682, 3681])).
% 1.86/2.11 tff(3684,plain,
% 1.86/2.11 (~b(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3683, 171, 160, 159, 3677])).
% 1.86/2.11 tff(3685,plain,
% 1.86/2.11 (r(z, s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[124, 3684])).
% 1.86/2.11 tff(3686,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(z))))))), introduced(assumption)).
% 1.86/2.11 tff(3687,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3688,plain,
% 1.86/2.11 (((~b(z, s(s(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(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~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)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3689,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3688])).
% 1.86/2.11 tff(3690,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3689, 3687])).
% 1.86/2.11 tff(3691,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3692,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3691, 3690])).
% 1.86/2.11 tff(3693,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3692, 171, 3686, 159, 3677])).
% 1.86/2.11 tff(3694,plain,
% 1.86/2.11 (r(s(s(s(s(z)))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[274, 3693])).
% 1.86/2.11 tff(3695,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3696,plain,
% 1.86/2.11 (((~b(z, s(s(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(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3697,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3696])).
% 1.86/2.11 tff(3698,plain,
% 1.86/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.86/2.11 inference(transitivity,[status(thm)],[3697, 3695])).
% 1.86/2.11 tff(3699,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3700,plain,
% 1.86/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3699, 3698])).
% 1.86/2.11 tff(3701,plain,
% 1.86/2.11 (~b(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3700, 171, 160, 159, 3677])).
% 1.86/2.11 tff(3702,plain,
% 1.86/2.11 (r(s(s(z)), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[157, 3701])).
% 1.86/2.11 tff(3703,plain,
% 1.86/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.11 inference(rewrite,[status(thm)],[])).
% 1.86/2.11 tff(3704,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.86/2.11 inference(quant_inst,[status(thm)],[])).
% 1.86/2.11 tff(3705,plain,
% 1.86/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 1.86/2.11 inference(modus_ponens,[status(thm)],[3704, 3703])).
% 1.86/2.11 tff(3706,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3705, 106, 637, 600, 569, 2118])).
% 1.86/2.11 tff(3707,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3708,plain,
% 1.86/2.11 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3707, 2118, 637, 600])).
% 1.86/2.11 tff(3709,plain,
% 1.86/2.11 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[2138, 2118, 95, 259, 600, 96])).
% 1.86/2.11 tff(3710,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[374, 3709, 3708, 355])).
% 1.86/2.11 tff(3711,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3712,plain,
% 1.86/2.11 ($false),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3711, 3702, 3694, 259, 3685, 96, 95])).
% 1.86/2.11 tff(3713,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(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(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.11 tff(3714,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3713, 3671, 94, 31, 259, 3669, 323])).
% 1.86/2.11 tff(3715,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[205, 3714])).
% 1.86/2.11 tff(3716,plain,
% 1.86/2.11 (~r(s(s(s(s(s(z))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[1398, 638, 95, 61])).
% 1.86/2.11 tff(3717,plain,
% 1.86/2.11 (b(s(s(s(s(s(z))))), z)),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[145, 3716])).
% 1.86/2.11 tff(3718,plain,
% 1.86/2.11 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[3713, 3717, 96, 95, 259, 3686, 323])).
% 1.86/2.11 tff(3719,plain,
% 1.86/2.11 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(unit_resolution,[status(thm)],[205, 3718])).
% 1.86/2.11 tff(3720,plain,
% 1.86/2.11 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(s(z))))))),
% 1.86/2.11 inference(monotonicity,[status(thm)],[3077])).
% 1.86/2.11 tff(3721,plain,
% 1.86/2.12 (b(s(z), s(s(s(s(s(z)))))) <=> b(s(z), elem!1)),
% 1.86/2.12 inference(symmetry,[status(thm)],[3720])).
% 1.86/2.12 tff(3722,plain,
% 1.86/2.12 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(s(z), elem!1))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3721])).
% 1.86/2.12 tff(3723,plain,
% 1.86/2.12 (~b(s(z), elem!1)),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[32, 3722])).
% 1.86/2.12 tff(3724,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1421, 3723])).
% 1.86/2.12 tff(3725,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3726,plain,
% 1.86/2.12 (~(elem!1 = s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3725, 1421, 32])).
% 1.86/2.12 tff(3727,plain,
% 1.86/2.12 (r(s(s(z)), elem!1)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[1416, 2116, 733])).
% 1.86/2.12 tff(3728,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3729,plain,
% 1.86/2.12 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3730,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3729])).
% 1.86/2.12 tff(3731,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3730, 3728])).
% 1.86/2.12 tff(3732,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3733,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3732, 3731])).
% 1.86/2.12 tff(3734,plain,
% 1.86/2.12 (~b(elem!1, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3733, 171, 323, 679, 259])).
% 1.86/2.12 tff(3735,plain,
% 1.86/2.12 (s(s(z)) = elem!1),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3105, 1479])).
% 1.86/2.12 tff(3736,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[2116, 3735])).
% 1.86/2.12 tff(3737,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3738,plain,
% 1.86/2.12 (~(elem!1 = s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3737, 2116])).
% 1.86/2.12 tff(3739,plain,
% 1.86/2.12 (r(elem!1, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3154, 3738, 3734])).
% 1.86/2.12 tff(3740,plain,
% 1.86/2.12 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.86/2.12 inference(symmetry,[status(thm)],[1615])).
% 1.86/2.12 tff(3741,assumption,(~b(elem!1, s(s(z)))), introduced(assumption)).
% 1.86/2.12 tff(3742,plain,
% 1.86/2.12 (r(elem!1, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3154, 3738, 3741])).
% 1.86/2.12 tff(3743,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3744,plain,
% 1.86/2.12 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3745,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3744])).
% 1.86/2.12 tff(3746,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3745, 3743])).
% 1.86/2.12 tff(3747,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3748,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3747, 3746])).
% 1.86/2.12 tff(3749,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3748, 106, 638, 3742, 637, 3727])).
% 1.86/2.12 tff(3750,plain,((s(s(z)) = elem!1) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3751,plain,
% 1.86/2.12 (~r(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3750, 2116, 638, 3734, 733])).
% 1.86/2.12 tff(3752,plain,
% 1.86/2.12 (b(s(s(z)), z)),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[157, 3751])).
% 1.86/2.12 tff(3753,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3754,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3755,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 1.86/2.12 tff(3756,plain,
% 1.86/2.12 (~r(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3755, 106, 638, 3739, 3727])).
% 1.86/2.12 tff(3757,plain,
% 1.86/2.12 (b(z, s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[124, 3756])).
% 1.86/2.12 tff(3758,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[215, 3757, 159, 3752])).
% 1.86/2.12 tff(3759,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[225, 3758])).
% 1.86/2.12 tff(3760,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3761,plain,
% 1.86/2.12 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3762,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3761])).
% 1.86/2.12 tff(3763,plain,
% 1.86/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3762, 3760])).
% 1.86/2.12 tff(3764,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3765,plain,
% 1.86/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3764, 3763])).
% 1.86/2.12 tff(3766,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3765, 106, 1403, 769, 396, 501])).
% 1.86/2.12 tff(3767,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3768,plain,
% 1.86/2.12 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3767, 3759, 3727, 501])).
% 1.86/2.12 tff(3769,plain,
% 1.86/2.12 (b(elem!1, s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[782, 3768, 1908])).
% 1.86/2.12 tff(3770,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3771,plain,
% 1.86/2.12 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3772,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 1.86/2.12 inference(monotonicity,[status(thm)],[3771])).
% 1.86/2.12 tff(3773,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 1.86/2.12 inference(transitivity,[status(thm)],[3772, 3770])).
% 1.86/2.12 tff(3774,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 1.86/2.12 inference(quant_inst,[status(thm)],[])).
% 1.86/2.12 tff(3775,plain,
% 1.86/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 1.86/2.12 inference(modus_ponens,[status(thm)],[3774, 3773])).
% 1.86/2.12 tff(3776,plain,
% 1.86/2.12 ($false),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3775, 171, 679, 1421, 840, 4])).
% 1.86/2.12 tff(3777,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.86/2.12 tff(3778,plain,
% 1.86/2.12 (~b(s(s(s(s(s(z))))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[3777, 3769, 679, 1421])).
% 1.86/2.12 tff(3779,plain,
% 1.86/2.12 (r(s(s(s(s(s(z))))), s(z))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[479, 3778])).
% 1.86/2.12 tff(3780,plain,
% 1.86/2.12 (~r(z, s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[486, 106, 96, 95, 3779])).
% 1.86/2.12 tff(3781,plain,
% 1.86/2.12 (b(z, s(s(s(s(s(z))))))),
% 1.86/2.12 inference(unit_resolution,[status(thm)],[498, 3780])).
% 1.86/2.12 tff(3782,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3783,plain,
% 1.86/2.12 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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)))),
% 1.86/2.12 inference(rewrite,[status(thm)],[])).
% 1.86/2.12 tff(3784,plain,
% 1.86/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[3783])).
% 1.96/2.12 tff(3785,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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)))),
% 1.96/2.12 inference(transitivity,[status(thm)],[3784, 3782])).
% 1.96/2.12 tff(3786,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 1.96/2.12 inference(quant_inst,[status(thm)],[])).
% 1.96/2.12 tff(3787,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))),
% 1.96/2.12 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 1.96/2.12 tff(3788,plain,
% 1.96/2.12 (~b(s(s(s(s(z)))), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[3787, 171, 3757, 3686, 159, 3781])).
% 1.96/2.12 tff(3789,plain,
% 1.96/2.12 (r(s(s(s(s(z)))), z)),
% 1.96/2.12 inference(unit_resolution,[status(thm)],[274, 3788])).
% 1.96/2.12 tff(3790,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(3791,plain,
% 1.96/2.12 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.12 inference(rewrite,[status(thm)],[])).
% 1.96/2.12 tff(3792,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.96/2.12 inference(monotonicity,[status(thm)],[3791])).
% 1.96/2.12 tff(3793,plain,
% 1.96/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.12 inference(transitivity,[status(thm)],[3792, 3790])).
% 1.96/2.12 tff(3794,plain,
% 1.96/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3795,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3794, 3793])).
% 1.96/2.13 tff(3796,plain,
% 1.96/2.13 (~b(elem!1, z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3795, 171, 3757, 3769, 159, 3781])).
% 1.96/2.13 tff(3797,plain,
% 1.96/2.13 (r(elem!1, z)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1567, 3796, 3385])).
% 1.96/2.13 tff(3798,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3799,plain,
% 1.96/2.13 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3800,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3799])).
% 1.96/2.13 tff(3801,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3800, 3798])).
% 1.96/2.13 tff(3802,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3803,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3802, 3801])).
% 1.96/2.13 tff(3804,plain,
% 1.96/2.13 (~r(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3803, 106, 638, 3797, 3789])).
% 1.96/2.13 tff(3805,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3806,plain,
% 1.96/2.13 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3807,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3806])).
% 1.96/2.13 tff(3808,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3807, 3805])).
% 1.96/2.13 tff(3809,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3810,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3809, 3808])).
% 1.96/2.13 tff(3811,plain,
% 1.96/2.13 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3810, 171, 3686, 83, 3769])).
% 1.96/2.13 tff(3812,plain,
% 1.96/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3813,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3814,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3813, 3812])).
% 1.96/2.13 tff(3815,plain,
% 1.96/2.13 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3814, 25, 3811])).
% 1.96/2.13 tff(3816,plain,
% 1.96/2.13 (s(s(s(s(z)))) = elem!1),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3815, 3804])).
% 1.96/2.13 tff(3817,plain,
% 1.96/2.13 (s(s(s(s(s(z))))) = s(elem!1)),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3816])).
% 1.96/2.13 tff(3818,plain,
% 1.96/2.13 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3817])).
% 1.96/2.13 tff(3819,plain,
% 1.96/2.13 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3818, 1615])).
% 1.96/2.13 tff(3820,plain,
% 1.96/2.13 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3819, 3740])).
% 1.96/2.13 tff(3821,plain,
% 1.96/2.13 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3820])).
% 1.96/2.13 tff(3822,plain,
% 1.96/2.13 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.96/2.13 inference(transitivity,[status(thm)],[49, 3272, 812])).
% 1.96/2.13 tff(3823,plain,
% 1.96/2.13 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3822])).
% 1.96/2.13 tff(3824,plain,
% 1.96/2.13 (s(s(s(z))) = s(elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[191, 3823, 1002])).
% 1.96/2.13 tff(3825,plain,
% 1.96/2.13 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3824])).
% 1.96/2.13 tff(3826,plain,
% 1.96/2.13 (s(s(z)) = elem!1),
% 1.96/2.13 inference(transitivity,[status(thm)],[341, 3825, 916])).
% 1.96/2.13 tff(3827,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[2116, 3826])).
% 1.96/2.13 tff(3828,plain,((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.13 tff(3829,plain,
% 1.96/2.13 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3828, 2116])).
% 1.96/2.13 tff(3830,plain,
% 1.96/2.13 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3829, 3821])).
% 1.96/2.13 tff(3831,plain,
% 1.96/2.13 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(elem!1), s(z))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3817])).
% 1.96/2.13 tff(3832,plain,
% 1.96/2.13 (r(s(elem!1), s(z))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3779, 3831])).
% 1.96/2.13 tff(3833,plain,
% 1.96/2.13 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1712, 3832, 95, 96, 3830])).
% 1.96/2.13 tff(3834,plain,
% 1.96/2.13 (b(s(s(s(elem!1))), s(z))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1807, 3833])).
% 1.96/2.13 tff(3835,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3836,plain,
% 1.96/2.13 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3837,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3836])).
% 1.96/2.13 tff(3838,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3837, 3835])).
% 1.96/2.13 tff(3839,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3840,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3839, 3838])).
% 1.96/2.13 tff(3841,plain,
% 1.96/2.13 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3840, 171, 323, 3834, 259])).
% 1.96/2.13 tff(3842,plain,
% 1.96/2.13 (r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1013, 3841])).
% 1.96/2.13 tff(3843,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3844,plain,
% 1.96/2.13 (((~r(s(s(z)), elem!1)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3845,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3844])).
% 1.96/2.13 tff(3846,plain,
% 1.96/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3845, 3843])).
% 1.96/2.13 tff(3847,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3848,plain,
% 1.96/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 1.96/2.13 tff(3849,plain,
% 1.96/2.13 (~r(s(s(s(elem!1))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3848, 106, 3842, 3739, 3727])).
% 1.96/2.13 tff(3850,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3851,plain,
% 1.96/2.13 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3852,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3851])).
% 1.96/2.13 tff(3853,plain,
% 1.96/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3852, 3850])).
% 1.96/2.13 tff(3854,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3855,plain,
% 1.96/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3854, 3853])).
% 1.96/2.13 tff(3856,plain,
% 1.96/2.13 (~b(s(s(s(elem!1))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3855, 171, 323, 3834, 679, 259])).
% 1.96/2.13 tff(3857,plain,
% 1.96/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.96/2.13 inference(rewrite,[status(thm)],[])).
% 1.96/2.13 tff(3858,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 1.96/2.13 inference(quant_inst,[status(thm)],[])).
% 1.96/2.13 tff(3859,plain,
% 1.96/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.96/2.13 inference(modus_ponens,[status(thm)],[3858, 3857])).
% 1.96/2.13 tff(3860,plain,
% 1.96/2.13 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3859, 25, 3856])).
% 1.96/2.13 tff(3861,plain,
% 1.96/2.13 (s(s(s(elem!1))) = elem!1),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[3860, 3849])).
% 1.96/2.13 tff(3862,plain,
% 1.96/2.13 (elem!1 = s(s(s(elem!1)))),
% 1.96/2.13 inference(symmetry,[status(thm)],[3861])).
% 1.96/2.13 tff(3863,plain,
% 1.96/2.13 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.96/2.13 inference(transitivity,[status(thm)],[3816, 3862])).
% 1.96/2.13 tff(3864,plain,
% 1.96/2.13 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3863])).
% 1.96/2.13 tff(3865,plain,
% 1.96/2.13 (s(s(s(z))) = s(s(elem!1))),
% 1.96/2.13 inference(transitivity,[status(thm)],[191, 3864, 812])).
% 1.96/2.13 tff(3866,plain,
% 1.96/2.13 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.96/2.13 inference(monotonicity,[status(thm)],[3865])).
% 1.96/2.13 tff(3867,plain,
% 1.96/2.13 (s(s(z)) = s(elem!1)),
% 1.96/2.13 inference(transitivity,[status(thm)],[341, 3866, 1002])).
% 1.96/2.13 tff(3868,plain,
% 1.96/2.13 ($false),
% 1.96/2.13 inference(unit_resolution,[status(thm)],[1552, 3867])).
% 1.96/2.13 tff(3869,plain,((s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(z, elem!1)) | (elem!1 = 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(z), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3870,plain,
% 1.96/2.14 (s(s(z)) = elem!1),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3869, 1421, 259, 679, 95, 96, 638, 3385, 3717, 3686, 83, 323, 3726, 501, 733])).
% 1.96/2.14 tff(3871,plain,
% 1.96/2.14 (s(s(s(z))) = s(elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3870])).
% 1.96/2.14 tff(3872,plain,
% 1.96/2.14 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3871])).
% 1.96/2.14 tff(3873,plain,
% 1.96/2.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3872])).
% 1.96/2.14 tff(3874,plain,
% 1.96/2.14 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3870])).
% 1.96/2.14 tff(3875,plain,
% 1.96/2.14 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3874])).
% 1.96/2.14 tff(3876,plain,
% 1.96/2.14 (~(s(s(s(elem!1))) = elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1008, 3875])).
% 1.96/2.14 tff(3877,plain,
% 1.96/2.14 (s(s(s(z))) = s(elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1418])).
% 1.96/2.14 tff(3878,plain,
% 1.96/2.14 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3877])).
% 1.96/2.14 tff(3879,plain,
% 1.96/2.14 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3878])).
% 1.96/2.14 tff(3880,plain,
% 1.96/2.14 (r(elem!1, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3879])).
% 1.96/2.14 tff(3881,plain,
% 1.96/2.14 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3880])).
% 1.96/2.14 tff(3882,plain,
% 1.96/2.14 ((~r(elem!1, s(s(s(elem!1))))) <=> (~r(elem!1, s(s(s(s(s(z)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3881])).
% 1.96/2.14 tff(3883,plain,
% 1.96/2.14 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[2891, 3882])).
% 1.96/2.14 tff(3884,plain,
% 1.96/2.14 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1418])).
% 1.96/2.14 tff(3885,plain,
% 1.96/2.14 (r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[501, 3884])).
% 1.96/2.14 tff(3886,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3885, 3883])).
% 1.96/2.14 tff(3887,plain,((~(s(s(z)) = elem!1)) | r(elem!1, s(s(s(elem!1)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3888,plain,
% 1.96/2.14 (r(elem!1, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3887, 3870, 501])).
% 1.96/2.14 tff(3889,plain,
% 1.96/2.14 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3872])).
% 1.96/2.14 tff(3890,plain,
% 1.96/2.14 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3889])).
% 1.96/2.14 tff(3891,plain,
% 1.96/2.14 (b(s(s(s(elem!1))), z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3717, 3890])).
% 1.96/2.14 tff(3892,plain,
% 1.96/2.14 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3889])).
% 1.96/2.14 tff(3893,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3892])).
% 1.96/2.14 tff(3894,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3893])).
% 1.96/2.14 tff(3895,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3872])).
% 1.96/2.14 tff(3896,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3686, 3895])).
% 1.96/2.14 tff(3897,plain,
% 1.96/2.14 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3896, 3894])).
% 1.96/2.14 tff(3898,plain,
% 1.96/2.14 (b(z, s(s(z))) <=> b(z, elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1418])).
% 1.96/2.14 tff(3899,plain,
% 1.96/2.14 (b(z, elem!1) <=> b(z, s(s(z)))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3898])).
% 1.96/2.14 tff(3900,plain,
% 1.96/2.14 ((~b(z, elem!1)) <=> (~b(z, s(s(z))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3899])).
% 1.96/2.14 tff(3901,plain,
% 1.96/2.14 (~b(z, s(s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[258, 3900])).
% 1.96/2.14 tff(3902,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[161, 3901])).
% 1.96/2.14 tff(3903,plain,((~(s(s(z)) = elem!1)) | (~b(z, s(s(z)))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3904,plain,
% 1.96/2.14 (~b(z, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3903, 3870, 258])).
% 1.96/2.14 tff(3905,plain,
% 1.96/2.14 (r(z, s(s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[124, 3904])).
% 1.96/2.14 tff(3906,plain,
% 1.96/2.14 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3889])).
% 1.96/2.14 tff(3907,plain,
% 1.96/2.14 (r(s(z), s(s(s(elem!1))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[61, 3906])).
% 1.96/2.14 tff(3908,plain,
% 1.96/2.14 (r(z, s(s(s(s(s(z)))))) <=> r(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3879])).
% 1.96/2.14 tff(3909,plain,
% 1.96/2.14 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3908])).
% 1.96/2.14 tff(3910,plain,
% 1.96/2.14 ((~r(z, s(s(s(elem!1))))) <=> (~r(z, s(s(s(s(s(z)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3909])).
% 1.96/2.14 tff(3911,plain,
% 1.96/2.14 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1418])).
% 1.96/2.14 tff(3912,plain,
% 1.96/2.14 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3911])).
% 1.96/2.14 tff(3913,plain,
% 1.96/2.14 (~(s(s(s(elem!1))) = elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1008, 3912])).
% 1.96/2.14 tff(3914,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.96/2.14 tff(3915,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.96/2.14 tff(3916,plain,
% 1.96/2.14 (~r(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3711, 637, 259, 600, 96, 95])).
% 1.96/2.14 tff(3917,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[274, 3916])).
% 1.96/2.14 tff(3918,plain,
% 1.96/2.14 (s(s(elem!1)) = s(s(s(s(z))))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3878])).
% 1.96/2.14 tff(3919,plain,
% 1.96/2.14 (b(s(s(elem!1)), z) <=> b(s(s(s(s(z)))), z)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3918])).
% 1.96/2.14 tff(3920,plain,
% 1.96/2.14 (b(s(s(s(s(z)))), z) <=> b(s(s(elem!1)), z)),
% 1.96/2.14 inference(symmetry,[status(thm)],[3919])).
% 1.96/2.14 tff(3921,plain,
% 1.96/2.14 (b(s(s(elem!1)), z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[2141, 3920])).
% 1.96/2.14 tff(3922,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.96/2.14 tff(3923,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3922, 3921])).
% 1.96/2.14 tff(3924,plain,(b(s(s(elem!1)), z) | (~b(s(s(s(s(z)))), z)) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3925,plain,
% 1.96/2.14 (b(s(s(elem!1)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3924, 3917, 1418])).
% 1.96/2.14 tff(3926,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.96/2.14 tff(3927,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.96/2.14 tff(3928,plain,
% 1.96/2.14 (s(s(s(elem!1))) = z),
% 1.96/2.14 inference(symmetry,[status(thm)],[3927])).
% 1.96/2.14 tff(3929,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[724, 3928])).
% 1.96/2.14 tff(3930,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3931,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 1.96/2.14 tff(3932,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3933,plain,
% 1.96/2.14 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3934,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3933])).
% 1.96/2.14 tff(3935,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[3934, 3932])).
% 1.96/2.14 tff(3936,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(3937,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3936, 3935])).
% 1.96/2.14 tff(3938,plain,
% 1.96/2.14 (~b(s(s(s(elem!1))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3937, 171, 1809, 679, 1421])).
% 1.96/2.14 tff(3939,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3859, 25, 3938, 3931])).
% 1.96/2.14 tff(3940,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3941,plain,
% 1.96/2.14 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3942,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3941])).
% 1.96/2.14 tff(3943,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)))),
% 1.96/2.14 inference(transitivity,[status(thm)],[3942, 3940])).
% 1.96/2.14 tff(3944,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(elem!1))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(3945,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 1.96/2.14 tff(3946,plain,
% 1.96/2.14 (~r(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3945, 106, 638, 1652, 3939])).
% 1.96/2.14 tff(3947,plain,
% 1.96/2.14 (b(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1593, 25, 3946, 3930])).
% 1.96/2.14 tff(3948,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3949,plain,
% 1.96/2.14 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3950,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3949])).
% 1.96/2.14 tff(3951,plain,
% 1.96/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[3950, 3948])).
% 1.96/2.14 tff(3952,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(3953,plain,
% 1.96/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3952, 3951])).
% 1.96/2.14 tff(3954,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3953, 171, 1809, 3947, 3914, 3915, 3926])).
% 1.96/2.14 tff(3955,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3956,plain,
% 1.96/2.14 (~b(s(s(s(elem!1))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3955, 3925, 3915, 3914, 638, 1652, 3913, 679, 1421])).
% 1.96/2.14 tff(3957,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1807, 3956])).
% 1.96/2.14 tff(3958,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3959,plain,
% 1.96/2.14 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3960,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3959])).
% 1.96/2.14 tff(3961,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.14 inference(transitivity,[status(thm)],[3960, 3958])).
% 1.96/2.14 tff(3962,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(3963,plain,
% 1.96/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 1.96/2.14 tff(3964,plain,
% 1.96/2.14 (~r(z, s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3963, 106, 3957, 96, 2231])).
% 1.96/2.14 tff(3965,plain,
% 1.96/2.14 (~r(z, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3964, 3910])).
% 1.96/2.14 tff(3966,plain,
% 1.96/2.14 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3879])).
% 1.96/2.14 tff(3967,plain,
% 1.96/2.14 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3966])).
% 1.96/2.14 tff(3968,plain,
% 1.96/2.14 (r(s(s(s(s(s(z))))), s(z))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3957, 3967])).
% 1.96/2.14 tff(3969,plain,
% 1.96/2.14 (b(s(s(s(z))), s(z)) <=> b(s(elem!1), s(z))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3877])).
% 1.96/2.14 tff(3970,plain,
% 1.96/2.14 (b(s(elem!1), s(z)) <=> b(s(s(s(z))), s(z))),
% 1.96/2.14 inference(symmetry,[status(thm)],[3969])).
% 1.96/2.14 tff(3971,plain,
% 1.96/2.14 (~(s(s(s(elem!1))) = s(elem!1))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1613, 1418, 701])).
% 1.96/2.14 tff(3972,plain,
% 1.96/2.14 (~(s(elem!1) = s(s(s(elem!1))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1620, 3971])).
% 1.96/2.14 tff(3973,plain,
% 1.96/2.14 (~r(s(elem!1), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1712, 3957, 95, 96, 3972])).
% 1.96/2.14 tff(3974,plain,
% 1.96/2.14 (b(s(elem!1), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1717, 3973, 701])).
% 1.96/2.14 tff(3975,plain,
% 1.96/2.14 (b(s(s(s(z))), s(z))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3974, 3970])).
% 1.96/2.14 tff(3976,plain,
% 1.96/2.14 (~b(s(s(s(s(z)))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[2702, 3975, 637, 259, 638, 95])).
% 1.96/2.14 tff(3977,plain,
% 1.96/2.14 (r(s(s(s(s(z)))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[321, 3976, 255])).
% 1.96/2.14 tff(3978,plain,
% 1.96/2.14 ((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1335, 415])).
% 1.96/2.14 tff(3979,plain,
% 1.96/2.14 (~b(z, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3978, 3977, 95, 96, 3968])).
% 1.96/2.14 tff(3980,plain,
% 1.96/2.14 (r(z, s(s(s(s(s(z))))))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[498, 3979])).
% 1.96/2.14 tff(3981,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3980, 3965])).
% 1.96/2.14 tff(3982,plain,((~r(s(s(z)), z)) | (~(s(s(z)) = elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(z, elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (s(elem!1) = s(z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(3983,plain,
% 1.96/2.14 (~r(s(s(z)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3982, 3870, 95, 96, 259, 638, 3907, 701, 3897, 3891, 3888, 679, 1421, 3905])).
% 1.96/2.14 tff(3984,plain,
% 1.96/2.14 (b(s(s(z)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[157, 3983])).
% 1.96/2.14 tff(3985,plain,
% 1.96/2.14 (r(s(s(z)), elem!1) <=> r(elem!1, elem!1)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3870])).
% 1.96/2.14 tff(3986,plain,
% 1.96/2.14 (r(elem!1, elem!1) <=> r(s(s(z)), elem!1)),
% 1.96/2.14 inference(symmetry,[status(thm)],[3985])).
% 1.96/2.14 tff(3987,plain,
% 1.96/2.14 ((~r(elem!1, elem!1)) <=> (~r(s(s(z)), elem!1))),
% 1.96/2.14 inference(monotonicity,[status(thm)],[3986])).
% 1.96/2.14 tff(3988,plain,
% 1.96/2.14 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.96/2.14 inference(bind,[status(th)],[])).
% 1.96/2.14 tff(3989,plain,
% 1.96/2.14 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.96/2.14 inference(quant_intro,[status(thm)],[3988])).
% 1.96/2.14 tff(3990,plain,
% 1.96/2.14 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(3991,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ri')).
% 1.96/2.14 tff(3992,plain,
% 1.96/2.14 (![X: $i] : (~r(X, X))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 1.96/2.14 tff(3993,plain,(
% 1.96/2.14 ![X: $i] : (~r(X, X))),
% 1.96/2.14 inference(skolemize,[status(sab)],[3992])).
% 1.96/2.14 tff(3994,plain,
% 1.96/2.14 (![X: $i] : (~r(X, X))),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3993, 3989])).
% 1.96/2.14 tff(3995,plain,
% 1.96/2.14 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 1.96/2.14 inference(quant_inst,[status(thm)],[])).
% 1.96/2.14 tff(3996,plain,
% 1.96/2.14 (~r(elem!1, elem!1)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3995, 3994])).
% 1.96/2.14 tff(3997,plain,
% 1.96/2.14 (~r(s(s(z)), elem!1)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[3996, 3987])).
% 1.96/2.14 tff(3998,plain,
% 1.96/2.14 (r(s(s(z)), z) <=> r(elem!1, z)),
% 1.96/2.14 inference(monotonicity,[status(thm)],[1418])).
% 1.96/2.14 tff(3999,plain,
% 1.96/2.14 (r(elem!1, z) <=> r(s(s(z)), z)),
% 1.96/2.14 inference(symmetry,[status(thm)],[3998])).
% 1.96/2.14 tff(4000,plain,
% 1.96/2.14 (r(s(s(z)), z)),
% 1.96/2.14 inference(modus_ponens,[status(thm)],[1554, 3999])).
% 1.96/2.14 tff(4001,plain,
% 1.96/2.14 ($false),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[152, 4000])).
% 1.96/2.14 tff(4002,plain,((~(s(s(z)) = elem!1)) | r(s(s(z)), z) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.14 tff(4003,plain,
% 1.96/2.14 (~r(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[4002, 3983, 3870])).
% 1.96/2.14 tff(4004,plain,
% 1.96/2.14 (b(elem!1, z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1567, 4003, 3385])).
% 1.96/2.14 tff(4005,plain,
% 1.96/2.14 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1801, 4004, 96, 259, 701, 95, 679, 3997, 3984, 638, 1440, 1552])).
% 1.96/2.14 tff(4006,plain,
% 1.96/2.14 (b(s(s(s(elem!1))), s(z))),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[1807, 4005])).
% 1.96/2.14 tff(4007,plain,
% 1.96/2.14 (~b(s(s(elem!1)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3955, 4006, 3897, 3891, 638, 3888, 3876, 679, 1421])).
% 1.96/2.14 tff(4008,plain,
% 1.96/2.14 (r(s(s(elem!1)), z)),
% 1.96/2.14 inference(unit_resolution,[status(thm)],[3025, 25, 816, 4007])).
% 1.96/2.14 tff(4009,plain,
% 1.96/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.96/2.14 inference(rewrite,[status(thm)],[])).
% 1.96/2.14 tff(4010,plain,
% 1.96/2.14 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4011,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4010])).
% 1.96/2.15 tff(4012,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4011, 4009])).
% 1.96/2.15 tff(4013,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4014,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4013, 4012])).
% 1.96/2.15 tff(4015,plain,
% 1.96/2.15 (~r(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4014, 106, 638, 95, 4008])).
% 1.96/2.15 tff(4016,plain,
% 1.96/2.15 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[3873])).
% 1.96/2.15 tff(4017,plain,
% 1.96/2.15 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(symmetry,[status(thm)],[4016])).
% 1.96/2.15 tff(4018,plain,
% 1.96/2.15 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(s(z), s(s(elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4017])).
% 1.96/2.15 tff(4019,plain,
% 1.96/2.15 (~b(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3924, 4007, 3870])).
% 1.96/2.15 tff(4020,plain,
% 1.96/2.15 (r(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[274, 4019])).
% 1.96/2.15 tff(4021,plain,
% 1.96/2.15 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2126, 4020, 95, 3905])).
% 1.96/2.15 tff(4022,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[321, 4021, 255])).
% 1.96/2.15 tff(4023,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[3889])).
% 1.96/2.15 tff(4024,plain,
% 1.96/2.15 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(symmetry,[status(thm)],[4023])).
% 1.96/2.15 tff(4025,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), s(z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4006, 4024])).
% 1.96/2.15 tff(4026,plain,
% 1.96/2.15 (~b(s(z), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[445, 4025, 4022, 259])).
% 1.96/2.15 tff(4027,plain,
% 1.96/2.15 (~b(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4026, 4018])).
% 1.96/2.15 tff(4028,plain,
% 1.96/2.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4029,plain,
% 1.96/2.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4030,plain,
% 1.96/2.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4029, 4028])).
% 1.96/2.15 tff(4031,plain,
% 1.96/2.15 (s(z) = s(s(elem!1))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4030, 25, 4027, 4015])).
% 1.96/2.15 tff(4032,plain,
% 1.96/2.15 (s(z) = s(s(s(s(z))))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4031, 3873])).
% 1.96/2.15 tff(4033,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[254, 4032])).
% 1.96/2.15 tff(4034,plain,((~b(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~r(z, s(z))) | (s(elem!1) = s(z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | b(s(s(z)), elem!1) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4035,plain,
% 1.96/2.15 (~b(s(z), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4034, 501, 95, 259, 679, 96, 701, 3385, 3686, 258, 638, 83, 323, 733, 32])).
% 1.96/2.15 tff(4036,plain,
% 1.96/2.15 (r(s(z), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1444, 4035, 1440])).
% 1.96/2.15 tff(4037,plain,
% 1.96/2.15 (~r(elem!1, s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1660, 4036, 96, 638])).
% 1.96/2.15 tff(4038,plain,
% 1.96/2.15 (~(s(s(z)) = elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3887, 4037, 501])).
% 1.96/2.15 tff(4039,plain,
% 1.96/2.15 (~(elem!1 = s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3737, 4038])).
% 1.96/2.15 tff(4040,plain,
% 1.96/2.15 (r(elem!1, s(s(z)))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3154, 4039, 3734])).
% 1.96/2.15 tff(4041,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4042,plain,
% 1.96/2.15 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4043,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4042])).
% 1.96/2.15 tff(4044,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4043, 4041])).
% 1.96/2.15 tff(4045,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4046,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4045, 4044])).
% 1.96/2.15 tff(4047,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4046, 106, 638, 4040, 95, 4036])).
% 1.96/2.15 tff(4048,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (s(elem!1) = s(z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | b(s(s(z)), elem!1) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4049,plain,
% 1.96/2.15 (~b(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4048, 733, 95, 96, 259, 638, 701, 3385, 3686, 258, 83, 323, 3719, 32])).
% 1.96/2.15 tff(4050,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[687, 4049, 1434, 676])).
% 1.96/2.15 tff(4051,plain,(b(s(s(z)), elem!1) | r(elem!1, s(z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (elem!1 = z) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | b(z, elem!1) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4052,plain,
% 1.96/2.15 (b(s(s(z)), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4051, 676, 31, 94, 259, 1465, 1535, 1553, 3669, 258, 83, 323, 32])).
% 1.96/2.15 tff(4053,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4054,plain,
% 1.96/2.15 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4055,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4054])).
% 1.96/2.15 tff(4056,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4055, 4053])).
% 1.96/2.15 tff(4057,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4058,plain,
% 1.96/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4057, 4056])).
% 1.96/2.15 tff(4059,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4058, 171, 323, 679, 259, 666])).
% 1.96/2.15 tff(4060,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4061,plain,
% 1.96/2.15 (~b(elem!1, s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4060, 4052, 259, 323])).
% 1.96/2.15 tff(4062,plain,
% 1.96/2.15 (elem!1 = s(z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[687, 4061, 676])).
% 1.96/2.15 tff(4063,plain,
% 1.96/2.15 (b(elem!1, z) <=> b(s(z), z)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.15 tff(4064,plain,
% 1.96/2.15 (b(s(z), z) <=> b(elem!1, z)),
% 1.96/2.15 inference(symmetry,[status(thm)],[4063])).
% 1.96/2.15 tff(4065,plain,
% 1.96/2.15 ((~b(s(z), z)) <=> (~b(elem!1, z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4064])).
% 1.96/2.15 tff(4066,plain,
% 1.96/2.15 (~b(elem!1, z)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[5, 4065])).
% 1.96/2.15 tff(4067,plain,
% 1.96/2.15 (r(z, elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[651, 695, 258])).
% 1.96/2.15 tff(4068,plain,
% 1.96/2.15 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1398, 4067, 95, 126])).
% 1.96/2.15 tff(4069,plain,
% 1.96/2.15 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[145, 4068])).
% 1.96/2.15 tff(4070,assumption,(~b(elem!1, z)), introduced(assumption)).
% 1.96/2.15 tff(4071,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3196, 106, 96, 126, 396, 1288])).
% 1.96/2.15 tff(4072,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4073,plain,
% 1.96/2.15 (~r(z, s(s(s(s(s(z))))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4072, 396, 126, 96])).
% 1.96/2.15 tff(4074,plain,
% 1.96/2.15 (b(z, s(s(s(s(s(z))))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[498, 4073])).
% 1.96/2.15 tff(4075,plain,
% 1.96/2.15 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.96/2.15 inference(commutativity,[status(thm)],[])).
% 1.96/2.15 tff(4076,plain,
% 1.96/2.15 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428, 2359])).
% 1.96/2.15 tff(4077,plain,
% 1.96/2.15 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4076, 4075])).
% 1.96/2.15 tff(4078,plain,
% 1.96/2.15 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 1.96/2.15 inference(symmetry,[status(thm)],[4077])).
% 1.96/2.15 tff(4079,plain,
% 1.96/2.15 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4078])).
% 1.96/2.15 tff(4080,plain,
% 1.96/2.15 (~(elem!1 = s(s(elem!1)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[344, 4079])).
% 1.96/2.15 tff(4081,plain,
% 1.96/2.15 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(monotonicity,[status(thm)],[2360])).
% 1.96/2.15 tff(4082,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.15 inference(symmetry,[status(thm)],[4081])).
% 1.96/2.15 tff(4083,plain,
% 1.96/2.15 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4082])).
% 1.96/2.15 tff(4084,plain,
% 1.96/2.15 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3787, 171, 161, 3686, 4069])).
% 1.96/2.15 tff(4085,plain,
% 1.96/2.15 (~b(s(s(s(s(z)))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4084, 4074])).
% 1.96/2.15 tff(4086,plain,
% 1.96/2.15 (~b(s(s(s(elem!1))), z)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4085, 4083])).
% 1.96/2.15 tff(4087,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3048, 4086])).
% 1.96/2.15 tff(4088,plain,
% 1.96/2.15 (~r(s(z), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3043, 4087, 95, 4067])).
% 1.96/2.15 tff(4089,plain,
% 1.96/2.15 (b(s(z), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2229, 4088])).
% 1.96/2.15 tff(4090,plain,
% 1.96/2.15 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[3032, 4089, 1428])).
% 1.96/2.15 tff(4091,plain,
% 1.96/2.15 (b(elem!1, s(s(s(s(z))))) <=> b(s(z), s(s(s(s(z)))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.15 tff(4092,plain,
% 1.96/2.15 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4091])).
% 1.96/2.15 tff(4093,assumption,(~b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.96/2.15 tff(4094,plain,
% 1.96/2.15 (~b(s(z), s(s(s(s(z)))))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4093, 4092])).
% 1.96/2.15 tff(4095,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[376, 4094])).
% 1.96/2.15 tff(4096,plain,(b(elem!1, s(s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4097,plain,
% 1.96/2.15 (b(elem!1, s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4096, 4090, 1428])).
% 1.96/2.15 tff(4098,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.15 tff(4099,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 1.96/2.15 inference(symmetry,[status(thm)],[4098])).
% 1.96/2.15 tff(4100,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[2360])).
% 1.96/2.15 tff(4101,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.15 tff(4102,plain,
% 1.96/2.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4101, 4100])).
% 1.96/2.15 tff(4103,plain,
% 1.96/2.15 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(s(z)))), s(z)))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4102])).
% 1.96/2.15 tff(4104,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.96/2.15 tff(4105,plain,
% 1.96/2.15 (r(elem!1, z)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1567, 3218, 4070])).
% 1.96/2.15 tff(4106,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4107,plain,
% 1.96/2.15 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4108,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4107])).
% 1.96/2.15 tff(4109,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4108, 4106])).
% 1.96/2.15 tff(4110,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4111,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4110, 4109])).
% 1.96/2.15 tff(4112,plain,
% 1.96/2.15 ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4111, 106])).
% 1.96/2.15 tff(4113,plain,
% 1.96/2.15 ($false),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4112, 4105, 4067, 3035, 4104])).
% 1.96/2.15 tff(4114,plain,((z = elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.96/2.15 tff(4115,plain,
% 1.96/2.15 (~r(s(s(s(elem!1))), elem!1)),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4114, 4087, 258, 695, 4070])).
% 1.96/2.15 tff(4116,plain,
% 1.96/2.15 (~r(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4115, 4103])).
% 1.96/2.15 tff(4117,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[319, 25, 4116, 255])).
% 1.96/2.15 tff(4118,plain,
% 1.96/2.15 (b(s(s(s(s(z)))), elem!1)),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4117, 4099])).
% 1.96/2.15 tff(4119,plain,
% 1.96/2.15 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[329, 171, 323, 259, 4117])).
% 1.96/2.15 tff(4120,plain,
% 1.96/2.15 (r(s(s(z)), s(s(s(s(z)))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[351, 4119])).
% 1.96/2.15 tff(4121,plain,
% 1.96/2.15 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.15 tff(4122,plain,
% 1.96/2.15 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.15 inference(symmetry,[status(thm)],[4121])).
% 1.96/2.15 tff(4123,plain,
% 1.96/2.15 (b(elem!1, s(s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[323, 4122])).
% 1.96/2.15 tff(4124,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4125,plain,
% 1.96/2.15 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4126,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 1.96/2.15 inference(monotonicity,[status(thm)],[4125])).
% 1.96/2.15 tff(4127,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 1.96/2.15 inference(transitivity,[status(thm)],[4126, 4124])).
% 1.96/2.15 tff(4128,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4129,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4128, 4127])).
% 1.96/2.15 tff(4130,plain,
% 1.96/2.15 (~r(s(z), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4129, 106, 96, 95, 3035])).
% 1.96/2.15 tff(4131,plain,
% 1.96/2.15 (b(s(z), s(s(s(elem!1))))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[2229, 4130])).
% 1.96/2.15 tff(4132,plain,
% 1.96/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4133,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.96/2.15 inference(quant_inst,[status(thm)],[])).
% 1.96/2.15 tff(4134,plain,
% 1.96/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 1.96/2.15 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 1.96/2.15 tff(4135,plain,
% 1.96/2.15 (~r(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[4134, 106, 96, 95, 3035])).
% 1.96/2.15 tff(4136,plain,
% 1.96/2.15 (b(s(s(s(elem!1))), s(z))),
% 1.96/2.15 inference(unit_resolution,[status(thm)],[1807, 4135])).
% 1.96/2.15 tff(4137,plain,
% 1.96/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.15 tff(4138,plain,
% 1.96/2.15 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.15 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4139,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4138])).
% 1.96/2.16 tff(4140,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4139, 4137])).
% 1.96/2.16 tff(4141,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4142,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4141, 4140])).
% 1.96/2.16 tff(4143,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4142, 171, 4136, 259, 1016, 4131])).
% 1.96/2.16 tff(4144,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(4145,plain,
% 1.96/2.16 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4144, 4087, 96, 259, 95])).
% 1.96/2.16 tff(4146,plain,
% 1.96/2.16 (r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1013, 4145])).
% 1.96/2.16 tff(4147,plain,
% 1.96/2.16 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2366, 4146, 1428])).
% 1.96/2.16 tff(4148,plain,
% 1.96/2.16 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[2359])).
% 1.96/2.16 tff(4149,plain,
% 1.96/2.16 ((~b(s(s(elem!1)), s(s(s(s(z)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4148])).
% 1.96/2.16 tff(4150,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.96/2.16 tff(4151,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4152,plain,
% 1.96/2.16 (((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4153,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4152])).
% 1.96/2.16 tff(4154,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4153, 4151])).
% 1.96/2.16 tff(4155,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4156,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4155, 4154])).
% 1.96/2.16 tff(4157,plain,
% 1.96/2.16 ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4156, 171])).
% 1.96/2.16 tff(4158,plain,
% 1.96/2.16 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4157, 4150, 1086, 2433])).
% 1.96/2.16 tff(4159,plain,
% 1.96/2.16 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4158, 4149])).
% 1.96/2.16 tff(4160,plain,
% 1.96/2.16 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1102, 25, 4159, 2264])).
% 1.96/2.16 tff(4161,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4162,plain,
% 1.96/2.16 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4163,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4162])).
% 1.96/2.16 tff(4164,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4163, 4161])).
% 1.96/2.16 tff(4165,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4166,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4165, 4164])).
% 1.96/2.16 tff(4167,plain,
% 1.96/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4166, 106, 569, 4160, 500])).
% 1.96/2.16 tff(4168,plain,
% 1.96/2.16 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1428])).
% 1.96/2.16 tff(4169,plain,
% 1.96/2.16 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(symmetry,[status(thm)],[4168])).
% 1.96/2.16 tff(4170,plain,
% 1.96/2.16 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1428, 2359])).
% 1.96/2.16 tff(4171,plain,
% 1.96/2.16 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4170, 4169])).
% 1.96/2.16 tff(4172,plain,
% 1.96/2.16 (b(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4150, 4171])).
% 1.96/2.16 tff(4173,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[946, 4172])).
% 1.96/2.16 tff(4174,plain,((~b(elem!1, s(s(elem!1)))) | b(elem!1, s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(4175,plain,
% 1.96/2.16 (b(elem!1, s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4174, 4150, 1428])).
% 1.96/2.16 tff(4176,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 1.96/2.16 tff(4177,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4178,plain,
% 1.96/2.16 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4179,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4178])).
% 1.96/2.16 tff(4180,plain,
% 1.96/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4179, 4177])).
% 1.96/2.16 tff(4181,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4182,plain,
% 1.96/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4181, 4180])).
% 1.96/2.16 tff(4183,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4182, 106, 569, 4160, 500])).
% 1.96/2.16 tff(4184,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(z)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2642, 4183])).
% 1.96/2.16 tff(4185,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4186,plain,
% 1.96/2.16 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4187,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4186])).
% 1.96/2.16 tff(4188,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.96/2.16 inference(transitivity,[status(thm)],[4187, 4185])).
% 1.96/2.16 tff(4189,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(z)))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4190,plain,
% 1.96/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4189, 4188])).
% 1.96/2.16 tff(4191,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4190, 171, 4176, 2705, 2038, 2740])).
% 1.96/2.16 tff(4192,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(4193,plain,
% 1.96/2.16 (~b(s(s(z)), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4192, 4184, 4176, 4175])).
% 1.96/2.16 tff(4194,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[979, 25, 4193, 4167, 82])).
% 1.96/2.16 tff(4195,plain,((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(4196,plain,
% 1.96/2.16 (~b(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4195, 4147, 4123, 4120, 1428, 4118, 4097])).
% 1.96/2.16 tff(4197,plain,
% 1.96/2.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4198,plain,
% 1.96/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 1.96/2.16 inference(quant_inst,[status(thm)],[])).
% 1.96/2.16 tff(4199,plain,
% 1.96/2.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4198, 4197])).
% 1.96/2.16 tff(4200,plain,
% 1.96/2.16 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4199, 25])).
% 1.96/2.16 tff(4201,plain,
% 1.96/2.16 (r(elem!1, s(s(elem!1)))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4200, 4196, 4080])).
% 1.96/2.16 tff(4202,plain,
% 1.96/2.16 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[1428, 2359])).
% 1.96/2.16 tff(4203,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.96/2.16 tff(4204,plain,
% 1.96/2.16 (r(s(z), s(s(s(z))))),
% 1.96/2.16 inference(modus_ponens,[status(thm)],[4203, 4202])).
% 1.96/2.16 tff(4205,plain,
% 1.96/2.16 ($false),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[1990, 4204])).
% 1.96/2.16 tff(4206,plain,((~r(elem!1, s(s(elem!1)))) | r(s(z), s(s(s(z)))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.16 tff(4207,plain,
% 1.96/2.16 (r(s(z), s(s(s(z))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[4206, 4201, 1428])).
% 1.96/2.16 tff(4208,plain,
% 1.96/2.16 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2612, 4207, 126, 396])).
% 1.96/2.16 tff(4209,plain,
% 1.96/2.16 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.16 inference(unit_resolution,[status(thm)],[2614, 4208])).
% 1.96/2.16 tff(4210,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4211,plain,
% 1.96/2.16 (((~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(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.96/2.16 inference(rewrite,[status(thm)],[])).
% 1.96/2.16 tff(4212,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 1.96/2.16 inference(monotonicity,[status(thm)],[4211])).
% 1.96/2.16 tff(4213,plain,
% 1.96/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4212, 4210])).
% 1.96/2.17 tff(4214,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4215,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4214, 4213])).
% 1.96/2.17 tff(4216,plain,
% 1.96/2.17 (~b(s(s(s(z))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4215, 171, 3686, 83, 4209, 4074])).
% 1.96/2.17 tff(4217,plain,
% 1.96/2.17 (r(s(s(s(z))), z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[953, 25, 194, 4216])).
% 1.96/2.17 tff(4218,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4219,plain,
% 1.96/2.17 (((~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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4220,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[4219])).
% 1.96/2.17 tff(4221,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4220, 4218])).
% 1.96/2.17 tff(4222,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4223,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4222, 4221])).
% 1.96/2.17 tff(4224,plain,
% 1.96/2.17 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4223, 171, 3686, 83, 4209])).
% 1.96/2.17 tff(4225,plain,
% 1.96/2.17 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2842, 4224, 2264])).
% 1.96/2.17 tff(4226,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
% 1.96/2.17 tff(4227,plain,
% 1.96/2.17 (s(s(s(z))) = s(s(s(s(z))))),
% 1.96/2.17 inference(symmetry,[status(thm)],[4226])).
% 1.96/2.17 tff(4228,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[2839, 4227])).
% 1.96/2.17 tff(4229,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(4230,plain,
% 1.96/2.17 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4229, 2264])).
% 1.96/2.17 tff(4231,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4232,plain,
% 1.96/2.17 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4233,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[4232])).
% 1.96/2.17 tff(4234,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4233, 4231])).
% 1.96/2.17 tff(4235,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4236,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(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))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4235, 4234])).
% 1.96/2.17 tff(4237,plain,
% 1.96/2.17 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4236, 171, 3686, 83, 4209])).
% 1.96/2.17 tff(4238,plain,
% 1.96/2.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4239,plain,
% 1.96/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4240,plain,
% 1.96/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4239, 4238])).
% 1.96/2.17 tff(4241,plain,
% 1.96/2.17 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4240, 25, 4237, 4230])).
% 1.96/2.17 tff(4242,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4243,plain,
% 1.96/2.17 (((~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(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(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4244,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[4243])).
% 1.96/2.17 tff(4245,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4244, 4242])).
% 1.96/2.17 tff(4246,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4247,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 1.96/2.17 tff(4248,plain,
% 1.96/2.17 (~b(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4247, 171, 3686, 83, 4074])).
% 1.96/2.17 tff(4249,plain,
% 1.96/2.17 (r(z, s(s(s(s(z)))))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[293, 4248])).
% 1.96/2.17 tff(4250,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4251,plain,
% 1.96/2.17 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4252,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[4251])).
% 1.96/2.17 tff(4253,plain,
% 1.96/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4252, 4250])).
% 1.96/2.17 tff(4254,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4255,plain,
% 1.96/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4254, 4253])).
% 1.96/2.17 tff(4256,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4255, 106, 4249, 4241, 4225, 4217])).
% 1.96/2.17 tff(4257,plain,((~r(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)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | b(z, elem!1) | (z = elem!1) | b(elem!1, z) | (~r(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(4258,plain,
% 1.96/2.17 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4257, 161, 83, 126, 1428, 323, 259, 95, 258, 695, 4070, 96, 3686])).
% 1.96/2.17 tff(4259,plain,
% 1.96/2.17 (b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[225, 4258])).
% 1.96/2.17 tff(4260,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4261,plain,
% 1.96/2.17 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), 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(z)), s(z))) | (~b(s(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)))),
% 1.96/2.17 inference(rewrite,[status(thm)],[])).
% 1.96/2.17 tff(4262,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 1.96/2.17 inference(monotonicity,[status(thm)],[4261])).
% 1.96/2.17 tff(4263,plain,
% 1.96/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.17 inference(transitivity,[status(thm)],[4262, 4260])).
% 1.96/2.17 tff(4264,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 1.96/2.17 inference(quant_inst,[status(thm)],[])).
% 1.96/2.17 tff(4265,plain,
% 1.96/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 1.96/2.17 inference(modus_ponens,[status(thm)],[4264, 4263])).
% 1.96/2.17 tff(4266,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4265, 171, 323, 259, 161, 4259, 4069])).
% 1.96/2.17 tff(4267,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~r(s(z), z)) | b(z, elem!1) | (z = elem!1) | b(elem!1, z) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.17 tff(4268,plain,
% 1.96/2.17 (b(elem!1, z)),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4267, 1428, 259, 83, 126, 323, 31, 258, 695, 161, 96, 3686])).
% 1.96/2.17 tff(4269,plain,
% 1.96/2.17 ($false),
% 1.96/2.17 inference(unit_resolution,[status(thm)],[4268, 4066])).
% 1.96/2.17 tff(4270,plain,((~(elem!1 = s(z))) | b(s(z), z) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | b(z, elem!1) | (z = elem!1) | (~b(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(4271,plain,
% 1.96/2.18 (~b(z, s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4270, 4062, 259, 83, 61, 323, 258, 1464, 5, 94, 3669])).
% 1.96/2.18 tff(4272,plain,
% 1.96/2.18 (r(z, s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[124, 4271])).
% 1.96/2.18 tff(4273,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[374, 3709, 355])).
% 1.96/2.18 tff(4274,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4275,plain,
% 1.96/2.18 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4276,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4275])).
% 1.96/2.18 tff(4277,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4276, 4274])).
% 1.96/2.18 tff(4278,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4279,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4278, 4277])).
% 1.96/2.18 tff(4280,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4279, 106, 600, 4273, 501, 2118])).
% 1.96/2.18 tff(4281,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(4282,plain,
% 1.96/2.18 (~r(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4281, 4272, 3715, 31, 259, 94])).
% 1.96/2.18 tff(4283,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[274, 4282])).
% 1.96/2.18 tff(4284,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[365, 356, 259, 323])).
% 1.96/2.18 tff(4285,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[321, 4284, 255])).
% 1.96/2.18 tff(4286,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4287,plain,
% 1.96/2.18 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4288,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4287])).
% 1.96/2.18 tff(4289,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4288, 4286])).
% 1.96/2.18 tff(4290,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4291,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4290, 4289])).
% 1.96/2.18 tff(4292,plain,
% 1.96/2.18 (~r(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4291, 106, 96, 3, 263])).
% 1.96/2.18 tff(4293,plain,
% 1.96/2.18 (b(s(s(s(s(z)))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[272, 25, 52, 4292])).
% 1.96/2.18 tff(4294,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4295,plain,
% 1.96/2.18 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4296,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4295])).
% 1.96/2.18 tff(4297,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4296, 4294])).
% 1.96/2.18 tff(4298,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4299,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4298, 4297])).
% 1.96/2.18 tff(4300,plain,
% 1.96/2.18 (~r(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4299, 106, 96, 3, 263])).
% 1.96/2.18 tff(4301,plain,
% 1.96/2.18 (b(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[291, 25, 4300, 286])).
% 1.96/2.18 tff(4302,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4303,plain,
% 1.96/2.18 (((~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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(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))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4304,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4303])).
% 1.96/2.18 tff(4305,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4304, 4302])).
% 1.96/2.18 tff(4306,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4307,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4306, 4305])).
% 1.96/2.18 tff(4308,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4307, 171, 3686, 83, 159, 4301, 4293])).
% 1.96/2.18 tff(4309,plain,((~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(4310,plain,
% 1.96/2.18 (~r(s(z), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4309, 4285, 83, 96, 3686, 159])).
% 1.96/2.18 tff(4311,plain,
% 1.96/2.18 (b(s(z), s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[454, 4310, 254])).
% 1.96/2.18 tff(4312,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4313,plain,
% 1.96/2.18 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4314,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4313])).
% 1.96/2.18 tff(4315,plain,
% 1.96/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4314, 4312])).
% 1.96/2.18 tff(4316,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4317,plain,
% 1.96/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4316, 4315])).
% 1.96/2.18 tff(4318,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4317, 171, 323, 259, 4311, 356])).
% 1.96/2.18 tff(4319,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(4320,plain,
% 1.96/2.18 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4319, 3671, 259, 83, 94, 3669, 323])).
% 1.96/2.18 tff(4321,plain,
% 1.96/2.18 (r(s(s(s(s(z)))), s(s(z)))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[374, 4320, 355])).
% 1.96/2.18 tff(4322,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4323,plain,
% 1.96/2.18 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(rewrite,[status(thm)],[])).
% 1.96/2.18 tff(4324,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4323])).
% 1.96/2.18 tff(4325,plain,
% 1.96/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(transitivity,[status(thm)],[4324, 4322])).
% 1.96/2.18 tff(4326,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.96/2.18 inference(quant_inst,[status(thm)],[])).
% 1.96/2.18 tff(4327,plain,
% 1.96/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4326, 4325])).
% 1.96/2.18 tff(4328,plain,
% 1.96/2.18 (~r(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4327, 106, 4272, 4321, 3715])).
% 1.96/2.18 tff(4329,plain,
% 1.96/2.18 (b(z, s(s(s(s(z)))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[293, 4328])).
% 1.96/2.18 tff(4330,plain,
% 1.96/2.18 ($false),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4307, 171, 3669, 83, 3671, 4329, 4283])).
% 1.96/2.18 tff(4331,plain,(r(elem!1, s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | b(z, elem!1) | b(s(z), z) | b(s(z), s(s(s(s(s(z)))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.18 tff(4332,plain,
% 1.96/2.18 (r(elem!1, s(z))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[4331, 323, 259, 83, 258, 5, 32, 84])).
% 1.96/2.18 tff(4333,plain,
% 1.96/2.18 (~r(z, elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1376, 4332, 94, 31])).
% 1.96/2.18 tff(4334,plain,
% 1.96/2.18 (z = elem!1),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[651, 4333, 258])).
% 1.96/2.18 tff(4335,plain,
% 1.96/2.18 (s(elem!1) = s(z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[703, 4334])).
% 1.96/2.18 tff(4336,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4334])).
% 1.96/2.18 tff(4337,plain,
% 1.96/2.18 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(symmetry,[status(thm)],[4336])).
% 1.96/2.18 tff(4338,plain,
% 1.96/2.18 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), z))),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4337])).
% 1.96/2.18 tff(4339,plain,
% 1.96/2.18 (r(s(z), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[1927, 4334, 31])).
% 1.96/2.18 tff(4340,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[2035, 4339, 4332, 61])).
% 1.96/2.18 tff(4341,plain,
% 1.96/2.18 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(modus_ponens,[status(thm)],[4340, 4338])).
% 1.96/2.18 tff(4342,plain,
% 1.96/2.18 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[145, 4341])).
% 1.96/2.18 tff(4343,plain,
% 1.96/2.18 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[3713, 4342, 94, 31, 259, 3669, 323])).
% 1.96/2.18 tff(4344,plain,
% 1.96/2.18 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.96/2.18 inference(unit_resolution,[status(thm)],[205, 4343])).
% 1.96/2.18 tff(4345,plain,
% 1.96/2.18 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 1.96/2.18 inference(monotonicity,[status(thm)],[4334])).
% 1.96/2.18 tff(4346,plain,
% 1.96/2.19 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 1.96/2.19 inference(symmetry,[status(thm)],[4345])).
% 1.96/2.19 tff(4347,plain,
% 1.96/2.19 (b(s(s(z)), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1382, 4332, 94, 259, 31, 258])).
% 1.96/2.19 tff(4348,plain,
% 1.96/2.19 (b(s(s(z)), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4347, 4346])).
% 1.96/2.19 tff(4349,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[672])).
% 1.96/2.19 tff(4350,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(symmetry,[status(thm)],[4349])).
% 1.96/2.19 tff(4351,plain,
% 1.96/2.19 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4350])).
% 1.96/2.19 tff(4352,plain,
% 1.96/2.19 (elem!1 = z),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[672, 262])).
% 1.96/2.19 tff(4353,plain,
% 1.96/2.19 (~r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2035, 1928, 730, 126])).
% 1.96/2.19 tff(4354,plain,
% 1.96/2.19 (b(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[853, 1899, 4353])).
% 1.96/2.19 tff(4355,plain,
% 1.96/2.19 (s(s(elem!1)) = s(s(z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[1930])).
% 1.96/2.19 tff(4356,plain,
% 1.96/2.19 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4355])).
% 1.96/2.19 tff(4357,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4356])).
% 1.96/2.19 tff(4358,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[672])).
% 1.96/2.19 tff(4359,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(transitivity,[status(thm)],[4358, 4357])).
% 1.96/2.19 tff(4360,plain,
% 1.96/2.19 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[672])).
% 1.96/2.19 tff(4361,plain,
% 1.96/2.19 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 1.96/2.19 inference(symmetry,[status(thm)],[4360])).
% 1.96/2.19 tff(4362,plain,
% 1.96/2.19 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), z))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4361])).
% 1.96/2.19 tff(4363,plain,
% 1.96/2.19 (~r(s(s(s(s(s(z))))), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4353, 4362])).
% 1.96/2.19 tff(4364,plain,
% 1.96/2.19 (b(s(s(s(s(s(z))))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[145, 4363])).
% 1.96/2.19 tff(4365,plain,
% 1.96/2.19 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3713, 4364, 96, 95, 259, 3686, 323])).
% 1.96/2.19 tff(4366,plain,
% 1.96/2.19 (r(s(s(z)), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[205, 4365])).
% 1.96/2.19 tff(4367,plain,
% 1.96/2.19 (r(z, s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[672])).
% 1.96/2.19 tff(4368,plain,
% 1.96/2.19 (r(elem!1, s(s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[600, 4367])).
% 1.96/2.19 tff(4369,plain,
% 1.96/2.19 (r(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3048, 3045])).
% 1.96/2.19 tff(4370,plain,
% 1.96/2.19 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4144, 4369, 96, 259, 95])).
% 1.96/2.19 tff(4371,plain,
% 1.96/2.19 (r(s(s(s(elem!1))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1013, 4370])).
% 1.96/2.19 tff(4372,plain,
% 1.96/2.19 (r(s(s(s(z))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[995, 4371, 710])).
% 1.96/2.19 tff(4373,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[923])).
% 1.96/2.19 tff(4374,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(symmetry,[status(thm)],[4373])).
% 1.96/2.19 tff(4375,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[930])).
% 1.96/2.19 tff(4376,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(transitivity,[status(thm)],[4375, 4374])).
% 1.96/2.19 tff(4377,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[837, 4376])).
% 1.96/2.19 tff(4378,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3045, 4377])).
% 1.96/2.19 tff(4379,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(elem!1))), z) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(4380,plain,
% 1.96/2.19 (~b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4379, 3045, 710])).
% 1.96/2.19 tff(4381,plain,
% 1.96/2.19 (r(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[804, 4380, 797])).
% 1.96/2.19 tff(4382,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4383,plain,
% 1.96/2.19 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4384,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4383])).
% 1.96/2.19 tff(4385,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[4384, 4382])).
% 1.96/2.19 tff(4386,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(4387,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4386, 4385])).
% 1.96/2.19 tff(4388,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4387, 106, 2463, 4381, 4372, 501])).
% 1.96/2.19 tff(4389,plain,(b(s(s(s(elem!1))), z) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = elem!1) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(4390,plain,
% 1.96/2.19 (b(s(s(s(elem!1))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4389, 4368, 4366, 1930, 1929, 96, 259, 95])).
% 1.96/2.19 tff(4391,plain,
% 1.96/2.19 (b(s(s(s(z))), elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4390, 4359])).
% 1.96/2.19 tff(4392,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4393,plain,
% 1.96/2.19 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4394,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4393])).
% 1.96/2.19 tff(4395,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[4394, 4392])).
% 1.96/2.19 tff(4396,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(4397,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4396, 4395])).
% 1.96/2.19 tff(4398,plain,
% 1.96/2.19 (~r(elem!1, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4397, 106, 730, 1446, 747])).
% 1.96/2.19 tff(4399,plain,
% 1.96/2.19 (b(elem!1, s(s(s(elem!1))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[942, 4398, 710])).
% 1.96/2.19 tff(4400,plain,
% 1.96/2.19 (b(elem!1, s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[948, 4399, 710])).
% 1.96/2.19 tff(4401,plain,
% 1.96/2.19 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2046, 4400, 839, 837])).
% 1.96/2.19 tff(4402,plain,
% 1.96/2.19 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1368, 4401])).
% 1.96/2.19 tff(4403,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4404,plain,
% 1.96/2.19 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4405,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4404])).
% 1.96/2.19 tff(4406,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[4405, 4403])).
% 1.96/2.19 tff(4407,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(4408,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4407, 4406])).
% 1.96/2.19 tff(4409,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4408, 106, 1446, 769, 126, 1357])).
% 1.96/2.19 tff(4410,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(4411,plain,
% 1.96/2.19 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4410, 4402, 126, 1446])).
% 1.96/2.19 tff(4412,plain,
% 1.96/2.19 (b(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[782, 4411, 1908])).
% 1.96/2.19 tff(4413,plain,
% 1.96/2.19 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[848, 4412, 837, 839])).
% 1.96/2.19 tff(4414,plain,
% 1.96/2.19 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[2614, 4413])).
% 1.96/2.19 tff(4415,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4416,plain,
% 1.96/2.19 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4417,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4416])).
% 1.96/2.19 tff(4418,plain,
% 1.96/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 1.96/2.19 inference(transitivity,[status(thm)],[4417, 4415])).
% 1.96/2.19 tff(4419,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 1.96/2.19 inference(quant_inst,[status(thm)],[])).
% 1.96/2.19 tff(4420,plain,
% 1.96/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4419, 4418])).
% 1.96/2.19 tff(4421,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4420, 106, 4414, 126, 4402, 747])).
% 1.96/2.19 tff(4422,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(4423,plain,
% 1.96/2.19 (~r(s(s(s(z))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4422, 4391, 126, 4354, 1895, 1928, 1930, 730])).
% 1.96/2.19 tff(4424,plain,
% 1.96/2.19 (b(s(s(s(z))), s(z))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1173, 4423])).
% 1.96/2.19 tff(4425,plain,
% 1.96/2.19 (~r(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[1308, 4424, 259, 323, 95, 730, 4352])).
% 1.96/2.19 tff(4426,plain,
% 1.96/2.19 (b(elem!1, s(s(s(s(s(z))))))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[782, 4425, 1895])).
% 1.96/2.19 tff(4427,plain,
% 1.96/2.19 (~b(s(s(s(s(z)))), elem!1)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[3810, 171, 3686, 83, 4426])).
% 1.96/2.19 tff(4428,plain,
% 1.96/2.19 (~b(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4427, 4351])).
% 1.96/2.19 tff(4429,plain,
% 1.96/2.19 (~r(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4281, 600, 4366, 95, 259, 96])).
% 1.96/2.19 tff(4430,plain,
% 1.96/2.19 (b(s(s(s(s(z)))), z)),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[274, 4429])).
% 1.96/2.19 tff(4431,plain,
% 1.96/2.19 ($false),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4430, 4428])).
% 1.96/2.19 tff(4432,plain,((~r(z, s(s(z)))) | (~(z = elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.96/2.19 tff(4433,plain,
% 1.96/2.19 (~r(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[4432, 4334, 3669, 83, 259, 323, 31, 4332, 61, 94])).
% 1.96/2.19 tff(4434,plain,
% 1.96/2.19 (b(z, s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[124, 4433])).
% 1.96/2.19 tff(4435,plain,
% 1.96/2.19 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[215, 4434, 4348, 4342])).
% 1.96/2.19 tff(4436,plain,
% 1.96/2.19 (r(s(s(s(s(s(z))))), s(s(z)))),
% 1.96/2.19 inference(unit_resolution,[status(thm)],[225, 4435])).
% 1.96/2.19 tff(4437,plain,
% 1.96/2.19 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4334])).
% 1.96/2.19 tff(4438,plain,
% 1.96/2.19 ((~(s(s(s(elem!1))) = z)) <=> (~(s(s(s(elem!1))) = elem!1))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4437])).
% 1.96/2.19 tff(4439,plain,
% 1.96/2.19 (~(s(s(s(elem!1))) = elem!1)),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[724, 4438])).
% 1.96/2.19 tff(4440,plain,
% 1.96/2.19 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4334])).
% 1.96/2.19 tff(4441,plain,
% 1.96/2.19 (b(elem!1, s(s(z)))),
% 1.96/2.19 inference(modus_ponens,[status(thm)],[4434, 4440])).
% 1.96/2.19 tff(4442,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4443,plain,
% 1.96/2.19 (((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.96/2.19 inference(rewrite,[status(thm)],[])).
% 1.96/2.19 tff(4444,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z))))))),
% 1.96/2.19 inference(monotonicity,[status(thm)],[4443])).
% 1.96/2.19 tff(4445,plain,
% 1.96/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z)))))),
% 1.96/2.20 inference(transitivity,[status(thm)],[4444, 4442])).
% 1.96/2.20 tff(4446,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.96/2.20 inference(quant_inst,[status(thm)],[])).
% 1.96/2.20 tff(4447,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(z))))),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[4446, 4445])).
% 1.96/2.20 tff(4448,plain,
% 1.96/2.20 (~b(s(s(s(elem!1))), elem!1)),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[4447, 171, 323, 259, 1016, 4176])).
% 1.96/2.20 tff(4449,plain,
% 1.96/2.20 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.20 inference(rewrite,[status(thm)],[])).
% 1.96/2.20 tff(4450,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 1.96/2.20 inference(monotonicity,[status(thm)],[4449])).
% 1.96/2.20 tff(4451,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.96/2.20 inference(transitivity,[status(thm)],[4450, 3835])).
% 1.96/2.20 tff(4452,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.96/2.20 inference(quant_inst,[status(thm)],[])).
% 1.96/2.20 tff(4453,plain,
% 1.96/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 1.96/2.20 inference(modus_ponens,[status(thm)],[4452, 4451])).
% 1.96/2.20 tff(4454,plain,
% 1.96/2.20 (~b(s(s(s(elem!1))), s(z))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[4453, 171, 323, 259, 1016])).
% 1.96/2.20 tff(4455,plain,
% 1.96/2.20 (r(s(s(s(elem!1))), s(z))),
% 1.96/2.20 inference(unit_resolution,[status(thm)],[1807, 4454])).
% 1.96/2.20 tff(4456,plain,
% 1.96/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4457,plain,
% 2.04/2.20 (((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4458,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4457])).
% 2.04/2.20 tff(4459,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4458, 4456])).
% 2.04/2.20 tff(4460,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4461,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4460, 4459])).
% 2.04/2.20 tff(4462,plain,
% 2.04/2.20 (~b(s(z), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4461, 171, 323, 259, 1016])).
% 2.04/2.20 tff(4463,plain,
% 2.04/2.20 (r(s(z), s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2229, 4462])).
% 2.04/2.20 tff(4464,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4465,plain,
% 2.04/2.20 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4466,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4465])).
% 2.04/2.20 tff(4467,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4466, 4464])).
% 2.04/2.20 tff(4468,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4469,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4468, 4467])).
% 2.04/2.20 tff(4470,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4469, 106, 4104, 1571, 730, 2231])).
% 2.04/2.20 tff(4471,plain,((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(4472,plain,
% 2.04/2.20 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4471, 4463, 730, 4455])).
% 2.04/2.20 tff(4473,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3859, 25, 4472, 4448, 3931])).
% 2.04/2.20 tff(4474,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(4475,plain,
% 2.04/2.20 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4474, 4441, 259, 323, 4332, 4439])).
% 2.04/2.20 tff(4476,plain,
% 2.04/2.20 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1013, 4475])).
% 2.04/2.20 tff(4477,plain,
% 2.04/2.20 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[995, 4476, 4335])).
% 2.04/2.20 tff(4478,plain,
% 2.04/2.20 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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)))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4479,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4478])).
% 2.04/2.20 tff(4480,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4479, 982])).
% 2.04/2.20 tff(4481,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4482,plain,
% 2.04/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4481, 4480])).
% 2.04/2.20 tff(4483,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4482, 106, 4477, 4436, 4344])).
% 2.04/2.20 tff(4484,plain,
% 2.04/2.20 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2614, 4483])).
% 2.04/2.20 tff(4485,plain,
% 2.04/2.20 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4334])).
% 2.04/2.20 tff(4486,plain,
% 2.04/2.20 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4485, 759])).
% 2.04/2.20 tff(4487,plain,
% 2.04/2.20 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4486])).
% 2.04/2.20 tff(4488,plain,
% 2.04/2.20 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[140, 4487])).
% 2.04/2.20 tff(4489,plain,
% 2.04/2.20 (elem!1 = z),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4334, 262])).
% 2.04/2.20 tff(4490,plain,
% 2.04/2.20 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.20 inference(transitivity,[status(thm)],[4486, 760])).
% 2.04/2.20 tff(4491,plain,
% 2.04/2.20 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4490])).
% 2.04/2.20 tff(4492,plain,
% 2.04/2.20 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[140, 4491])).
% 2.04/2.20 tff(4493,plain,
% 2.04/2.20 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[853, 4492, 4340])).
% 2.04/2.20 tff(4494,plain,
% 2.04/2.20 (~(s(s(s(z))) = elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[788, 4334])).
% 2.04/2.20 tff(4495,plain,
% 2.04/2.20 (~r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[2054, 747, 1446, 730])).
% 2.04/2.20 tff(4496,plain,
% 2.04/2.20 (~b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4422, 747, 126, 839, 1908, 1446, 710, 730])).
% 2.04/2.20 tff(4497,plain,
% 2.04/2.20 ($false),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[804, 4496, 4495, 797])).
% 2.04/2.20 tff(4498,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(z))) = elem!1) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.20 tff(4499,plain,
% 2.04/2.20 (~r(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4498, 4494, 61, 4493, 4488, 4339, 4335, 4332])).
% 2.04/2.20 tff(4500,plain,
% 2.04/2.20 (b(s(s(s(z))), s(z))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1173, 4499])).
% 2.04/2.20 tff(4501,plain,
% 2.04/2.20 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[1308, 4500, 259, 323, 31, 4332, 4489])).
% 2.04/2.20 tff(4502,plain,
% 2.04/2.20 (b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[782, 4501, 4488])).
% 2.04/2.20 tff(4503,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4504,plain,
% 2.04/2.20 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4505,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4504])).
% 2.04/2.20 tff(4506,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4505, 4503])).
% 2.04/2.20 tff(4507,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4508,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4507, 4506])).
% 2.04/2.20 tff(4509,plain,
% 2.04/2.20 (~b(elem!1, s(s(s(z))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4508, 171, 3669, 83, 4502, 4484])).
% 2.04/2.20 tff(4510,plain,
% 2.04/2.20 (~b(elem!1, s(s(s(elem!1))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[948, 4509, 4335])).
% 2.04/2.20 tff(4511,plain,
% 2.04/2.20 (s(s(elem!1)) = s(s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4335])).
% 2.04/2.20 tff(4512,plain,
% 2.04/2.20 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4511])).
% 2.04/2.20 tff(4513,plain,
% 2.04/2.20 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4512])).
% 2.04/2.20 tff(4514,plain,
% 2.04/2.20 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4513, 4512])).
% 2.04/2.20 tff(4515,plain,
% 2.04/2.20 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4514, 1125])).
% 2.04/2.20 tff(4516,plain,
% 2.04/2.20 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4515])).
% 2.04/2.20 tff(4517,plain,
% 2.04/2.20 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4516])).
% 2.04/2.20 tff(4518,plain,
% 2.04/2.20 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[2264, 4517])).
% 2.04/2.20 tff(4519,plain,
% 2.04/2.20 (~b(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[848, 4502, 4484, 4493])).
% 2.04/2.20 tff(4520,plain,
% 2.04/2.20 (r(s(s(s(z))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[804, 4519, 4494])).
% 2.04/2.20 tff(4521,plain,
% 2.04/2.20 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4334])).
% 2.04/2.20 tff(4522,plain,
% 2.04/2.20 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4521])).
% 2.04/2.20 tff(4523,plain,
% 2.04/2.20 (~(s(s(s(s(z)))) = elem!1)),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[52, 4522])).
% 2.04/2.20 tff(4524,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4525,plain,
% 2.04/2.20 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(rewrite,[status(thm)],[])).
% 2.04/2.20 tff(4526,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4525])).
% 2.04/2.20 tff(4527,plain,
% 2.04/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.04/2.20 inference(transitivity,[status(thm)],[4526, 4524])).
% 2.04/2.20 tff(4528,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.04/2.20 inference(quant_inst,[status(thm)],[])).
% 2.04/2.20 tff(4529,plain,
% 2.04/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(modus_ponens,[status(thm)],[4528, 4527])).
% 2.04/2.20 tff(4530,plain,
% 2.04/2.20 ((~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4529, 171, 4441, 3669, 4493])).
% 2.04/2.20 tff(4531,plain,
% 2.04/2.20 (~b(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[4530, 4502])).
% 2.04/2.20 tff(4532,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.20 inference(unit_resolution,[status(thm)],[3814, 25, 4531, 4523])).
% 2.04/2.20 tff(4533,plain,
% 2.04/2.20 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.04/2.20 inference(symmetry,[status(thm)],[713])).
% 2.04/2.20 tff(4534,plain,
% 2.04/2.20 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4533])).
% 2.04/2.20 tff(4535,plain,
% 2.04/2.20 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.04/2.20 inference(symmetry,[status(thm)],[4534])).
% 2.04/2.20 tff(4536,plain,
% 2.04/2.20 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4533])).
% 2.04/2.20 tff(4537,plain,
% 2.04/2.20 ((~r(s(s(s(s(z)))), s(z))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.04/2.20 inference(monotonicity,[status(thm)],[4536])).
% 2.04/2.20 tff(4538,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.04/2.20 tff(4539,plain,
% 2.04/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4540,plain,
% 2.04/2.21 (((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4541,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4540])).
% 2.04/2.21 tff(4542,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4541, 4539])).
% 2.04/2.21 tff(4543,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4544,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4543, 4542])).
% 2.04/2.21 tff(4545,plain,
% 2.04/2.21 ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4544, 106, 1446, 1426])).
% 2.04/2.21 tff(4546,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4545, 4538])).
% 2.04/2.21 tff(4547,plain,
% 2.04/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4546, 4537])).
% 2.04/2.21 tff(4548,plain,
% 2.04/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1066, 4547])).
% 2.04/2.21 tff(4549,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4548, 4535])).
% 2.04/2.21 tff(4550,plain,
% 2.04/2.21 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4533, 930])).
% 2.04/2.21 tff(4551,plain,
% 2.04/2.21 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[4550])).
% 2.04/2.21 tff(4552,plain,
% 2.04/2.21 ((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4551])).
% 2.04/2.21 tff(4553,plain,
% 2.04/2.21 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[1133, 4552])).
% 2.04/2.21 tff(4554,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4555,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4556,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4555, 4554])).
% 2.04/2.21 tff(4557,plain,
% 2.04/2.21 ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4556, 106, 2049, 1426])).
% 2.04/2.21 tff(4558,plain,
% 2.04/2.21 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4557, 4538])).
% 2.04/2.21 tff(4559,plain,
% 2.04/2.21 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4240, 25, 4558])).
% 2.04/2.21 tff(4560,plain,
% 2.04/2.21 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4559, 4553])).
% 2.04/2.21 tff(4561,plain,
% 2.04/2.21 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.04/2.21 inference(commutativity,[status(thm)],[])).
% 2.04/2.21 tff(4562,plain,
% 2.04/2.21 ((s(z) = s(s(s(z)))) <=> (s(z) = s(s(s(elem!1))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[930])).
% 2.04/2.21 tff(4563,plain,
% 2.04/2.21 ((s(z) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(z))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4562, 4561])).
% 2.04/2.21 tff(4564,plain,
% 2.04/2.21 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 2.04/2.21 inference(symmetry,[status(thm)],[4563])).
% 2.04/2.21 tff(4565,plain,
% 2.04/2.21 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4564])).
% 2.04/2.21 tff(4566,plain,
% 2.04/2.21 (~(s(z) = s(s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[818, 4565])).
% 2.04/2.21 tff(4567,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4568,plain,
% 2.04/2.21 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4569,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4568])).
% 2.04/2.21 tff(4570,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4569, 4567])).
% 2.04/2.21 tff(4571,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4572,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4571, 4570])).
% 2.04/2.21 tff(4573,plain,
% 2.04/2.21 (~r(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4572, 106, 1446, 2049, 1426])).
% 2.04/2.21 tff(4574,plain,
% 2.04/2.21 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1994, 25, 4573])).
% 2.04/2.21 tff(4575,plain,
% 2.04/2.21 (b(s(z), s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4574, 4566])).
% 2.04/2.21 tff(4576,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4577,plain,
% 2.04/2.21 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4578,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4577])).
% 2.04/2.21 tff(4579,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4578, 4576])).
% 2.04/2.21 tff(4580,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4581,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4580, 4579])).
% 2.04/2.21 tff(4582,plain,
% 2.04/2.21 ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4581, 171, 1188, 4575])).
% 2.04/2.21 tff(4583,plain,
% 2.04/2.21 (~b(s(s(s(s(z)))), s(z))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4582, 4560])).
% 2.04/2.21 tff(4584,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4583, 4549])).
% 2.04/2.21 tff(4585,plain,((~r(s(s(s(s(z)))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4586,plain,
% 2.04/2.21 (~r(elem!1, s(s(s(z))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4585, 4532, 4339, 4520, 4518, 4500, 4335])).
% 2.04/2.21 tff(4587,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[942, 4586, 4510, 4335])).
% 2.04/2.21 tff(4588,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | b(z, elem!1) | b(s(z), z) | b(s(z), s(s(s(s(s(z)))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4589,plain,
% 2.04/2.21 (~b(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4588, 259, 83, 258, 5, 32, 84])).
% 2.04/2.21 tff(4590,plain,
% 2.04/2.21 (r(s(z), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[550, 4589])).
% 2.04/2.21 tff(4591,plain,
% 2.04/2.21 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[1398, 638, 95, 126])).
% 2.04/2.21 tff(4592,plain,
% 2.04/2.21 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[145, 4591])).
% 2.04/2.21 tff(4593,plain,
% 2.04/2.21 (~r(s(s(z)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[646, 638, 554, 95])).
% 2.04/2.21 tff(4594,plain,
% 2.04/2.21 (b(s(s(z)), z)),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[157, 4593])).
% 2.04/2.21 tff(4595,plain,
% 2.04/2.21 (~b(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[179, 160, 1, 159])).
% 2.04/2.21 tff(4596,plain,
% 2.04/2.21 (r(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[124, 4595])).
% 2.04/2.21 tff(4597,plain,
% 2.04/2.21 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[608, 4596, 95, 554])).
% 2.04/2.21 tff(4598,plain,
% 2.04/2.21 (b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[351, 4597])).
% 2.04/2.21 tff(4599,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4600,plain,
% 2.04/2.21 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4601,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4600])).
% 2.04/2.21 tff(4602,plain,
% 2.04/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4601, 4599])).
% 2.04/2.21 tff(4603,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4604,plain,
% 2.04/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4603, 4602])).
% 2.04/2.21 tff(4605,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4604, 171, 3686, 83, 160, 4598])).
% 2.04/2.21 tff(4606,plain,((~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(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4607,plain,
% 2.04/2.21 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4606, 4594, 83, 95, 554, 3686, 4592])).
% 2.04/2.21 tff(4608,plain,
% 2.04/2.21 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[205, 4607])).
% 2.04/2.21 tff(4609,plain,
% 2.04/2.21 (~r(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[624, 4608, 96, 554])).
% 2.04/2.21 tff(4610,plain,
% 2.04/2.21 (b(z, s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[124, 4609])).
% 2.04/2.21 tff(4611,plain,
% 2.04/2.21 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[215, 4610, 4594, 4592])).
% 2.04/2.21 tff(4612,plain,
% 2.04/2.21 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[225, 4611])).
% 2.04/2.21 tff(4613,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4614,plain,
% 2.04/2.21 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~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(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.21 inference(rewrite,[status(thm)],[])).
% 2.04/2.21 tff(4615,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.04/2.21 inference(monotonicity,[status(thm)],[4614])).
% 2.04/2.21 tff(4616,plain,
% 2.04/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.21 inference(transitivity,[status(thm)],[4615, 4613])).
% 2.04/2.21 tff(4617,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.04/2.21 inference(quant_inst,[status(thm)],[])).
% 2.04/2.21 tff(4618,plain,
% 2.04/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.21 inference(modus_ponens,[status(thm)],[4617, 4616])).
% 2.04/2.21 tff(4619,plain,
% 2.04/2.21 ($false),
% 2.04/2.21 inference(unit_resolution,[status(thm)],[4618, 106, 554, 126, 4612, 4608])).
% 2.04/2.21 tff(4620,plain,((~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.21 tff(4621,plain,
% 2.04/2.22 (~r(z, elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4620, 4590, 61, 94, 83, 31, 3669])).
% 2.04/2.22 tff(4622,plain,
% 2.04/2.22 (z = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[651, 4621, 258])).
% 2.04/2.22 tff(4623,plain,
% 2.04/2.22 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4622])).
% 2.04/2.22 tff(4624,plain,
% 2.04/2.22 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 2.04/2.22 inference(symmetry,[status(thm)],[4623])).
% 2.04/2.22 tff(4625,plain,
% 2.04/2.22 (r(elem!1, s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[691, 4622, 84])).
% 2.04/2.22 tff(4626,plain,
% 2.04/2.22 (b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1382, 4625, 94, 259, 31, 258])).
% 2.04/2.22 tff(4627,plain,
% 2.04/2.22 (b(s(s(z)), z)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4626, 4624])).
% 2.04/2.22 tff(4628,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), z) <=> r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4622])).
% 2.04/2.22 tff(4629,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), z)),
% 2.04/2.22 inference(symmetry,[status(thm)],[4628])).
% 2.04/2.22 tff(4630,plain,
% 2.04/2.22 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4629])).
% 2.04/2.22 tff(4631,plain,
% 2.04/2.22 (r(s(z), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1927, 4622, 31])).
% 2.04/2.22 tff(4632,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[2035, 4625, 4631, 61])).
% 2.04/2.22 tff(4633,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4632, 4630])).
% 2.04/2.22 tff(4634,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[145, 4633])).
% 2.04/2.22 tff(4635,plain,
% 2.04/2.22 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4606, 4634, 83, 31, 4590, 3669, 4627])).
% 2.04/2.22 tff(4636,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[205, 4635])).
% 2.04/2.22 tff(4637,plain,
% 2.04/2.22 (~r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[624, 4636, 94, 4590])).
% 2.04/2.22 tff(4638,plain,
% 2.04/2.22 (b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[124, 4637])).
% 2.04/2.22 tff(4639,plain,
% 2.04/2.22 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[215, 4638, 4627, 4634])).
% 2.04/2.22 tff(4640,plain,
% 2.04/2.22 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[225, 4639])).
% 2.04/2.22 tff(4641,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4618, 106, 4590, 61, 4640, 4636])).
% 2.04/2.22 tff(4642,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(z, elem!1) | b(z, s(z)) | b(s(z), z) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4643,plain,
% 2.04/2.22 (~b(s(s(z)), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4642, 258, 83, 84, 5, 32])).
% 2.04/2.22 tff(4644,plain,
% 2.04/2.22 (r(s(s(z)), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[244, 4643])).
% 2.04/2.22 tff(4645,plain,
% 2.04/2.22 (~r(s(s(z)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[149, 106, 94, 4644, 31])).
% 2.04/2.22 tff(4646,plain,
% 2.04/2.22 (b(s(s(z)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[157, 4645])).
% 2.04/2.22 tff(4647,plain,
% 2.04/2.22 (~r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[112, 106, 94, 4644, 31])).
% 2.04/2.22 tff(4648,plain,
% 2.04/2.22 (b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[124, 4647])).
% 2.04/2.22 tff(4649,plain,
% 2.04/2.22 (~(s(s(z)) = elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[3903, 4648, 258])).
% 2.04/2.22 tff(4650,plain,
% 2.04/2.22 (~r(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[112, 106, 94, 2, 95])).
% 2.04/2.22 tff(4651,plain,
% 2.04/2.22 (b(z, s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[124, 4650])).
% 2.04/2.22 tff(4652,plain,
% 2.04/2.22 (~r(s(s(z)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[149, 106, 94, 2, 95])).
% 2.04/2.22 tff(4653,plain,
% 2.04/2.22 (b(s(s(z)), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[157, 4652])).
% 2.04/2.22 tff(4654,plain,
% 2.04/2.22 ((s(s(z)) = z) <=> (s(s(z)) = elem!1)),
% 2.04/2.22 inference(monotonicity,[status(thm)],[672])).
% 2.04/2.22 tff(4655,plain,
% 2.04/2.22 ((s(s(z)) = elem!1) <=> (s(s(z)) = z)),
% 2.04/2.22 inference(symmetry,[status(thm)],[4654])).
% 2.04/2.22 tff(4656,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4657,plain,
% 2.04/2.22 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4658,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4657])).
% 2.04/2.22 tff(4659,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4658, 4656])).
% 2.04/2.22 tff(4660,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4661,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4660, 4659])).
% 2.04/2.22 tff(4662,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4661, 106, 730, 2, 95, 1403])).
% 2.04/2.22 tff(4663,plain,((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4664,plain,
% 2.04/2.22 (~r(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4663, 1896, 95, 2])).
% 2.04/2.22 tff(4665,plain,
% 2.04/2.22 (s(s(z)) = elem!1),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1416, 4664, 733])).
% 2.04/2.22 tff(4666,plain,
% 2.04/2.22 (s(s(z)) = z),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4665, 4655])).
% 2.04/2.22 tff(4667,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[118, 4666])).
% 2.04/2.22 tff(4668,plain,((~(z = elem!1)) | b(s(s(z)), elem!1) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4669,plain,
% 2.04/2.22 (b(s(s(z)), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4668, 672, 95, 2, 84])).
% 2.04/2.22 tff(4670,plain,
% 2.04/2.22 (b(z, s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[672])).
% 2.04/2.22 tff(4671,plain,
% 2.04/2.22 (b(elem!1, s(s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4651, 4670])).
% 2.04/2.22 tff(4672,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[143, 25, 140, 757])).
% 2.04/2.22 tff(4673,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~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)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4674,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4675,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 2.04/2.22 tff(4676,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4675, 106, 2, 95, 502])).
% 2.04/2.22 tff(4677,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[225, 4676])).
% 2.04/2.22 tff(4678,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[213, 171, 125, 158, 4677, 4672])).
% 2.04/2.22 tff(4679,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4680,plain,
% 2.04/2.22 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4679, 2, 95, 94])).
% 2.04/2.22 tff(4681,plain,
% 2.04/2.22 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[479, 4680])).
% 2.04/2.22 tff(4682,plain,
% 2.04/2.22 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.04/2.22 inference(symmetry,[status(thm)],[4356])).
% 2.04/2.22 tff(4683,plain,
% 2.04/2.22 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4682])).
% 2.04/2.22 tff(4684,plain,
% 2.04/2.22 ((~r(s(s(s(z))), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4683])).
% 2.04/2.22 tff(4685,plain,
% 2.04/2.22 (r(s(z), elem!1)),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[95, 1921])).
% 2.04/2.22 tff(4686,plain,
% 2.04/2.22 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4687,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4686])).
% 2.04/2.22 tff(4688,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4687, 2050])).
% 2.04/2.22 tff(4689,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4690,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4689, 4688])).
% 2.04/2.22 tff(4691,plain,
% 2.04/2.22 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4690, 106, 730, 1446])).
% 2.04/2.22 tff(4692,plain,
% 2.04/2.22 (~r(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4691, 747])).
% 2.04/2.22 tff(4693,plain,
% 2.04/2.22 (b(s(s(s(z))), elem!1)),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[804, 4692, 797])).
% 2.04/2.22 tff(4694,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4695,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4696,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4695, 4694])).
% 2.04/2.22 tff(4697,plain,
% 2.04/2.22 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4696, 106, 2, 1446])).
% 2.04/2.22 tff(4698,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4697, 747])).
% 2.04/2.22 tff(4699,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[995, 4698, 710])).
% 2.04/2.22 tff(4700,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1013, 4699])).
% 2.04/2.22 tff(4701,plain,
% 2.04/2.22 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4700, 1015])).
% 2.04/2.22 tff(4702,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4703,plain,
% 2.04/2.22 (((~b(elem!1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4704,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4703])).
% 2.04/2.22 tff(4705,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4704, 4702])).
% 2.04/2.22 tff(4706,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4707,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4706, 4705])).
% 2.04/2.22 tff(4708,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4707, 171, 666, 4176, 4701, 4693])).
% 2.04/2.22 tff(4709,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~(s(elem!1) = s(z))) | (s(s(s(z))) = elem!1) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4710,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4709, 4671, 666, 1930, 1929, 2, 4685, 1896])).
% 2.04/2.22 tff(4711,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4710, 4684])).
% 2.04/2.22 tff(4712,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1807, 4711])).
% 2.04/2.22 tff(4713,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[930])).
% 2.04/2.22 tff(4714,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(symmetry,[status(thm)],[4713])).
% 2.04/2.22 tff(4715,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[1809, 4714])).
% 2.04/2.22 tff(4716,plain,
% 2.04/2.22 ($false),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1168, 4715])).
% 2.04/2.22 tff(4717,plain,(b(s(s(s(z))), s(z)) | (~b(s(s(s(elem!1))), s(z))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.22 tff(4718,plain,
% 2.04/2.22 (b(s(s(s(z))), s(z))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4717, 4712, 1930])).
% 2.04/2.22 tff(4719,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[1270])).
% 2.04/2.22 tff(4720,plain,
% 2.04/2.22 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(symmetry,[status(thm)],[4719])).
% 2.04/2.22 tff(4721,plain,
% 2.04/2.22 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[745, 710])).
% 2.04/2.22 tff(4722,plain,
% 2.04/2.22 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1284, 1275, 323, 4, 710])).
% 2.04/2.22 tff(4723,plain,
% 2.04/2.22 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[878, 4722, 4721])).
% 2.04/2.22 tff(4724,plain,
% 2.04/2.22 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4723, 4720])).
% 2.04/2.22 tff(4725,plain,
% 2.04/2.22 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[820, 710])).
% 2.04/2.22 tff(4726,plain,
% 2.04/2.22 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[826, 4725])).
% 2.04/2.22 tff(4727,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4728,plain,
% 2.04/2.22 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4729,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4728])).
% 2.04/2.22 tff(4730,plain,
% 2.04/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4729, 4727])).
% 2.04/2.22 tff(4731,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4732,plain,
% 2.04/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4731, 4730])).
% 2.04/2.22 tff(4733,plain,
% 2.04/2.22 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4732, 171, 1188, 1275, 4])).
% 2.04/2.22 tff(4734,plain,
% 2.04/2.22 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[835, 4733, 4726])).
% 2.04/2.22 tff(4735,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4736,plain,
% 2.04/2.22 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(rewrite,[status(thm)],[])).
% 2.04/2.22 tff(4737,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.22 inference(monotonicity,[status(thm)],[4736])).
% 2.04/2.22 tff(4738,plain,
% 2.04/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.22 inference(transitivity,[status(thm)],[4737, 4735])).
% 2.04/2.22 tff(4739,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.04/2.22 inference(quant_inst,[status(thm)],[])).
% 2.04/2.22 tff(4740,plain,
% 2.04/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(modus_ponens,[status(thm)],[4739, 4738])).
% 2.04/2.22 tff(4741,plain,
% 2.04/2.22 ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4740, 106, 2027, 4734])).
% 2.04/2.22 tff(4742,plain,
% 2.04/2.22 (~r(s(s(s(z))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[4741, 4724])).
% 2.04/2.22 tff(4743,plain,
% 2.04/2.22 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[995, 4742, 710])).
% 2.04/2.22 tff(4744,plain,
% 2.04/2.22 (b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.22 inference(unit_resolution,[status(thm)],[1013, 4743])).
% 2.04/2.23 tff(4745,plain,
% 2.04/2.23 (b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4744, 1015])).
% 2.04/2.23 tff(4746,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4747,plain,
% 2.04/2.23 (((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4748,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4747])).
% 2.04/2.23 tff(4749,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4748, 4746])).
% 2.04/2.23 tff(4750,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4751,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 2.04/2.23 tff(4752,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4751, 171, 323, 666, 4176, 1188, 2705])).
% 2.04/2.23 tff(4753,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4754,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4753, 1188, 666, 4176, 323])).
% 2.04/2.23 tff(4755,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4754, 4745])).
% 2.04/2.23 tff(4756,plain,((~b(s(s(s(z))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4757,plain,
% 2.04/2.23 (~b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4756, 2027, 710, 1188, 4, 666, 4176, 323])).
% 2.04/2.23 tff(4758,plain,
% 2.04/2.23 (r(s(z), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[60, 4757])).
% 2.04/2.23 tff(4759,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[2033, 106, 730, 1446, 2027, 4758])).
% 2.04/2.23 tff(4760,plain,((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4761,plain,
% 2.04/2.23 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4760, 1896, 4685, 1930, 4718, 4681, 666, 4671, 323])).
% 2.04/2.23 tff(4762,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[853, 4761, 1899])).
% 2.04/2.23 tff(4763,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4764,plain,
% 2.04/2.23 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4765,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4764])).
% 2.04/2.23 tff(4766,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4765, 4763])).
% 2.04/2.23 tff(4767,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4768,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4767, 4766])).
% 2.04/2.23 tff(4769,plain,
% 2.04/2.23 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4768, 171, 666, 4671, 4762])).
% 2.04/2.23 tff(4770,plain,
% 2.04/2.23 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[225, 4769])).
% 2.04/2.23 tff(4771,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4753, 4718, 666, 4671, 323])).
% 2.04/2.23 tff(4772,plain,
% 2.04/2.23 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1020, 4771, 1930])).
% 2.04/2.23 tff(4773,plain,
% 2.04/2.23 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1013, 4772])).
% 2.04/2.23 tff(4774,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[995, 4773, 1930])).
% 2.04/2.23 tff(4775,plain,
% 2.04/2.23 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[820, 1930])).
% 2.04/2.23 tff(4776,plain,
% 2.04/2.23 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[826, 4775])).
% 2.04/2.23 tff(4777,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4778,plain,
% 2.04/2.23 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4779,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4778])).
% 2.04/2.23 tff(4780,plain,
% 2.04/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4779, 4777])).
% 2.04/2.23 tff(4781,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4782,plain,
% 2.04/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4781, 4780])).
% 2.04/2.23 tff(4783,plain,
% 2.04/2.23 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4782, 171, 323, 666, 4718, 4762, 4681])).
% 2.04/2.23 tff(4784,plain,
% 2.04/2.23 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[835, 4783, 4776])).
% 2.04/2.23 tff(4785,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4786,plain,
% 2.04/2.23 (((~r(s(s(z)), s(z))) | (~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)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4787,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4786])).
% 2.04/2.23 tff(4788,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4787, 4785])).
% 2.04/2.23 tff(4789,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4790,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4789, 4788])).
% 2.04/2.23 tff(4791,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4790, 106, 2, 4784, 4774, 4770])).
% 2.04/2.23 tff(4792,plain,((~(z = elem!1)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~r(s(z), z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4793,plain,
% 2.04/2.23 (~b(s(z), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4792, 4669, 95, 2, 672, 84])).
% 2.04/2.23 tff(4794,plain,
% 2.04/2.23 (r(s(z), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[550, 4793])).
% 2.04/2.23 tff(4795,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4796,plain,
% 2.04/2.23 (((~r(s(s(z)), s(z))) | (~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(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.23 inference(rewrite,[status(thm)],[])).
% 2.04/2.23 tff(4797,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[4796])).
% 2.04/2.23 tff(4798,plain,
% 2.04/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.23 inference(transitivity,[status(thm)],[4797, 4795])).
% 2.04/2.23 tff(4799,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~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))))))))),
% 2.04/2.23 inference(quant_inst,[status(thm)],[])).
% 2.04/2.23 tff(4800,plain,
% 2.04/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4799, 4798])).
% 2.04/2.23 tff(4801,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4800, 106, 554, 2, 126, 396])).
% 2.04/2.23 tff(4802,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4803,plain,
% 2.04/2.23 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4802, 4794, 2, 126])).
% 2.04/2.23 tff(4804,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[225, 4803])).
% 2.04/2.23 tff(4805,plain,
% 2.04/2.23 (~b(s(s(s(s(s(z))))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[215, 4804, 4653, 4651])).
% 2.04/2.23 tff(4806,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(monotonicity,[status(thm)],[672])).
% 2.04/2.23 tff(4807,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), z)),
% 2.04/2.23 inference(symmetry,[status(thm)],[4806])).
% 2.04/2.23 tff(4808,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[839, 4807])).
% 2.04/2.23 tff(4809,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[138, 4808])).
% 2.04/2.23 tff(4810,plain,((~b(s(s(s(s(s(z))))), elem!1)) | b(s(s(s(s(s(z))))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4811,plain,
% 2.04/2.23 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4810, 4805, 672])).
% 2.04/2.23 tff(4812,plain,
% 2.04/2.23 (s(s(s(s(s(z))))) = elem!1),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[853, 4811, 2036])).
% 2.04/2.23 tff(4813,plain,
% 2.04/2.23 (elem!1 = s(s(s(s(s(z)))))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4812, 759])).
% 2.04/2.23 tff(4814,plain,
% 2.04/2.23 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4679, 2, 94, 95])).
% 2.04/2.23 tff(4815,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[479, 4814])).
% 2.04/2.23 tff(4816,plain,
% 2.04/2.23 (b(elem!1, s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.23 inference(monotonicity,[status(thm)],[3077])).
% 2.04/2.23 tff(4817,plain,
% 2.04/2.23 (b(s(s(s(s(s(z))))), s(z)) <=> b(elem!1, s(z))),
% 2.04/2.23 inference(symmetry,[status(thm)],[4816])).
% 2.04/2.23 tff(4818,plain,
% 2.04/2.23 (b(elem!1, s(z))),
% 2.04/2.23 inference(modus_ponens,[status(thm)],[4, 4817])).
% 2.04/2.23 tff(4819,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 2.04/2.23 tff(4820,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4819, 4818])).
% 2.04/2.23 tff(4821,plain,((~(elem!1 = s(s(s(s(s(z))))))) | b(elem!1, s(z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4822,plain,
% 2.04/2.23 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4821, 683, 4815])).
% 2.04/2.23 tff(4823,plain,
% 2.04/2.23 ($false),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4822, 4813])).
% 2.04/2.23 tff(4824,plain,((~(z = elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.23 tff(4825,plain,
% 2.04/2.23 (~(z = elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[4824, 4644, 61, 31, 84])).
% 2.04/2.23 tff(4826,plain,
% 2.04/2.23 (r(z, elem!1)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[651, 4825, 258])).
% 2.04/2.23 tff(4827,plain,
% 2.04/2.23 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.23 inference(unit_resolution,[status(thm)],[1398, 4826, 31, 61])).
% 2.04/2.23 tff(4828,plain,
% 2.04/2.24 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[145, 4827])).
% 2.04/2.24 tff(4829,plain,
% 2.04/2.24 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[215, 4828, 4646, 4648])).
% 2.04/2.24 tff(4830,plain,
% 2.04/2.24 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[225, 4829])).
% 2.04/2.24 tff(4831,plain,
% 2.04/2.24 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[179, 4828, 4646, 4648])).
% 2.04/2.24 tff(4832,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[205, 4831])).
% 2.04/2.24 tff(4833,plain,
% 2.04/2.24 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4072, 4830, 61, 94])).
% 2.04/2.24 tff(4834,plain,
% 2.04/2.24 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3251, 4833, 4826])).
% 2.04/2.24 tff(4835,plain,
% 2.04/2.24 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[498, 4833])).
% 2.04/2.24 tff(4836,plain,
% 2.04/2.24 (~(elem!1 = z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[697, 4825])).
% 2.04/2.24 tff(4837,plain,
% 2.04/2.24 (~r(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1376, 4826, 94, 31])).
% 2.04/2.24 tff(4838,plain,
% 2.04/2.24 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4679, 4644, 94, 31])).
% 2.04/2.24 tff(4839,plain,
% 2.04/2.24 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[479, 4838])).
% 2.04/2.24 tff(4840,plain,
% 2.04/2.24 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3767, 1403, 501, 396])).
% 2.04/2.24 tff(4841,plain,
% 2.04/2.24 (b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[782, 4840, 1908])).
% 2.04/2.24 tff(4842,plain,
% 2.04/2.24 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[1428])).
% 2.04/2.24 tff(4843,plain,
% 2.04/2.24 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(symmetry,[status(thm)],[4842])).
% 2.04/2.24 tff(4844,plain,
% 2.04/2.24 ((~b(s(z), s(s(s(s(s(z))))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4843])).
% 2.04/2.24 tff(4845,plain,
% 2.04/2.24 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[32, 4844])).
% 2.04/2.24 tff(4846,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[840, 4845])).
% 2.04/2.24 tff(4847,plain,((~(elem!1 = s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4848,plain,
% 2.04/2.24 (~(elem!1 = s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4847, 4841, 32])).
% 2.04/2.24 tff(4849,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[687, 4848, 676])).
% 2.04/2.24 tff(4850,plain,
% 2.04/2.24 (~r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4802, 396, 2, 61])).
% 2.04/2.24 tff(4851,plain,
% 2.04/2.24 (b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[550, 4850])).
% 2.04/2.24 tff(4852,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4853,plain,
% 2.04/2.24 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4854,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4853])).
% 2.04/2.24 tff(4855,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4854, 4852])).
% 2.04/2.24 tff(4856,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4857,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4856, 4855])).
% 2.04/2.24 tff(4858,plain,
% 2.04/2.24 (~b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4857, 171, 4851, 161, 4841, 4, 1313])).
% 2.04/2.24 tff(4859,plain,
% 2.04/2.24 (r(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1567, 4858, 3385])).
% 2.04/2.24 tff(4860,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4861,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4862,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4861, 4860])).
% 2.04/2.24 tff(4863,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4862, 106, 1554, 2, 1446, 1403])).
% 2.04/2.24 tff(4864,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4865,plain,
% 2.04/2.24 (~r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4864, 4859, 2, 1403])).
% 2.04/2.24 tff(4866,plain,
% 2.04/2.24 (~(s(z) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1439, 4848])).
% 2.04/2.24 tff(4867,plain,
% 2.04/2.24 (b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1444, 4866, 4865])).
% 2.04/2.24 tff(4868,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3777, 4867, 4849, 4, 4841])).
% 2.04/2.24 tff(4869,plain,((~r(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | r(elem!1, s(z)) | b(s(z), s(s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (elem!1 = z) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4870,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4869, 4839, 4837, 32, 4644, 4836, 4648, 4835, 4834, 4832, 4830])).
% 2.04/2.24 tff(4871,plain,
% 2.04/2.24 (b(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1416, 4870, 4649])).
% 2.04/2.24 tff(4872,plain,
% 2.04/2.24 ((~b(s(s(z)), s(z))) <=> (~b(s(s(z)), elem!1))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[1430])).
% 2.04/2.24 tff(4873,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 2.04/2.24 tff(4874,plain,
% 2.04/2.24 (~b(s(s(z)), elem!1)),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4873, 4872])).
% 2.04/2.24 tff(4875,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[666, 4874])).
% 2.04/2.24 tff(4876,plain,((~(elem!1 = s(z))) | (~b(s(s(z)), elem!1)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4877,plain,
% 2.04/2.24 (~(elem!1 = s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4876, 4871, 4643])).
% 2.04/2.24 tff(4878,plain,
% 2.04/2.24 (~(s(z) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1439, 4877])).
% 2.04/2.24 tff(4879,plain,
% 2.04/2.24 (~r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4802, 4830, 4644, 61])).
% 2.04/2.24 tff(4880,plain,
% 2.04/2.24 (b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[550, 4879])).
% 2.04/2.24 tff(4881,plain,
% 2.04/2.24 (b(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[687, 4877, 4837])).
% 2.04/2.24 tff(4882,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4883,plain,
% 2.04/2.24 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4884,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4883])).
% 2.04/2.24 tff(4885,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4884, 4882])).
% 2.04/2.24 tff(4886,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4887,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4886, 4885])).
% 2.04/2.24 tff(4888,plain,
% 2.04/2.24 ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4887, 171])).
% 2.04/2.24 tff(4889,plain,
% 2.04/2.24 (~b(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4888, 4881, 4880, 4871])).
% 2.04/2.24 tff(4890,plain,
% 2.04/2.24 (r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1444, 4889, 4878])).
% 2.04/2.24 tff(4891,plain,
% 2.04/2.24 (~r(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1562, 4890, 94, 4826])).
% 2.04/2.24 tff(4892,plain,
% 2.04/2.24 (b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1567, 4891, 4836])).
% 2.04/2.24 tff(4893,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4894,plain,
% 2.04/2.24 (((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4895,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4894])).
% 2.04/2.24 tff(4896,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4895, 4893])).
% 2.04/2.24 tff(4897,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(z, s(s(z)))) | (~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4898,plain,
% 2.04/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4897, 4896])).
% 2.04/2.24 tff(4899,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4898, 171, 4892, 4871, 4648, 4646])).
% 2.04/2.24 tff(4900,plain,(b(z, elem!1) | b(s(z), s(s(s(s(s(z)))))) | b(z, s(z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4901,plain,
% 2.04/2.24 (b(z, elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4900, 84, 32, 83, 5])).
% 2.04/2.24 tff(4902,plain,
% 2.04/2.24 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[135, 94, 95, 126])).
% 2.04/2.24 tff(4903,plain,
% 2.04/2.24 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[145, 4902])).
% 2.04/2.24 tff(4904,plain,
% 2.04/2.24 (~r(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[234, 94, 126, 95])).
% 2.04/2.24 tff(4905,plain,
% 2.04/2.24 (b(s(s(z)), s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[244, 4904])).
% 2.04/2.24 tff(4906,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 2.04/2.24 tff(4907,plain,
% 2.04/2.24 (r(z, s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[124, 4906])).
% 2.04/2.24 tff(4908,plain,
% 2.04/2.24 (b(z, s(s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[3137, 3899])).
% 2.04/2.24 tff(4909,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4906, 4908])).
% 2.04/2.24 tff(4910,plain,((~(s(s(z)) = elem!1)) | b(z, s(s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4911,plain,
% 2.04/2.24 (~(s(s(z)) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4910, 4906, 3137])).
% 2.04/2.24 tff(4912,plain,
% 2.04/2.24 (~r(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1411, 554, 94, 600])).
% 2.04/2.24 tff(4913,plain,
% 2.04/2.24 (b(s(s(z)), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1416, 4912, 2116])).
% 2.04/2.24 tff(4914,plain,
% 2.04/2.24 (b(z, s(z)) <=> b(z, elem!1)),
% 2.04/2.24 inference(monotonicity,[status(thm)],[1435])).
% 2.04/2.24 tff(4915,plain,
% 2.04/2.24 (b(z, elem!1) <=> b(z, s(z))),
% 2.04/2.24 inference(symmetry,[status(thm)],[4914])).
% 2.04/2.24 tff(4916,plain,
% 2.04/2.24 (b(z, s(z))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[3137, 4915])).
% 2.04/2.24 tff(4917,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[84, 4916])).
% 2.04/2.24 tff(4918,plain,((~(s(z) = elem!1)) | b(z, s(z)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4919,plain,
% 2.04/2.24 (~(s(z) = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4918, 84, 3137])).
% 2.04/2.24 tff(4920,plain,
% 2.04/2.24 (~r(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2952, 554, 600, 95])).
% 2.04/2.24 tff(4921,plain,
% 2.04/2.24 (b(s(s(z)), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[157, 4920])).
% 2.04/2.24 tff(4922,plain,
% 2.04/2.24 (~b(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3227, 4913, 3137, 4921])).
% 2.04/2.24 tff(4923,plain,
% 2.04/2.24 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[624, 554, 94, 600])).
% 2.04/2.24 tff(4924,plain,
% 2.04/2.24 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[205, 4923])).
% 2.04/2.24 tff(4925,plain,
% 2.04/2.24 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4606, 4924, 83, 95, 4903, 554, 4921])).
% 2.04/2.24 tff(4926,plain,
% 2.04/2.24 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3668, 4925])).
% 2.04/2.24 tff(4927,plain,
% 2.04/2.24 (~(z = elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[2066, 4926, 126, 83, 4905, 4924, 95, 4913, 84])).
% 2.04/2.24 tff(4928,plain,
% 2.04/2.24 (~(elem!1 = z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[697, 4927])).
% 2.04/2.24 tff(4929,plain,
% 2.04/2.24 (r(elem!1, z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[1567, 4928, 4922])).
% 2.04/2.24 tff(4930,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4931,plain,
% 2.04/2.24 (((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4932,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z)))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4931])).
% 2.04/2.24 tff(4933,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4932, 4930])).
% 2.04/2.24 tff(4934,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4935,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z)))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4934, 4933])).
% 2.04/2.24 tff(4936,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4935, 106, 1554, 730, 96, 95])).
% 2.04/2.24 tff(4937,plain,((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4938,plain,
% 2.04/2.24 (~r(elem!1, s(z))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4937, 4929, 94, 95])).
% 2.04/2.24 tff(4939,plain,
% 2.04/2.24 (r(s(z), elem!1)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3074, 4938, 4905, 4919, 4913])).
% 2.04/2.24 tff(4940,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4941,plain,
% 2.04/2.24 (((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 2.04/2.24 inference(rewrite,[status(thm)],[])).
% 2.04/2.24 tff(4942,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 2.04/2.24 inference(monotonicity,[status(thm)],[4941])).
% 2.04/2.24 tff(4943,plain,
% 2.04/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 2.04/2.24 inference(transitivity,[status(thm)],[4942, 4940])).
% 2.04/2.24 tff(4944,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.04/2.24 inference(quant_inst,[status(thm)],[])).
% 2.04/2.24 tff(4945,plain,
% 2.04/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 2.04/2.24 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 2.04/2.24 tff(4946,plain,
% 2.04/2.24 ($false),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4945, 106, 4929, 94, 95, 4939])).
% 2.04/2.24 tff(4947,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(z, s(z)) | (~b(z, elem!1)) | (s(s(z)) = elem!1) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.24 tff(4948,plain,
% 2.04/2.24 (~r(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4947, 4911, 126, 83, 84, 3137, 95, 4907])).
% 2.04/2.24 tff(4949,plain,
% 2.04/2.24 (b(s(z), s(s(z)))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[550, 4948])).
% 2.04/2.24 tff(4950,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[544, 4949, 4905, 83, 126, 94, 95])).
% 2.04/2.24 tff(4951,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3668, 4950])).
% 2.04/2.24 tff(4952,plain,
% 2.04/2.24 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[3713, 4951, 94, 95, 4905, 4949, 4903])).
% 2.04/2.24 tff(4953,plain,
% 2.04/2.24 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[205, 4952])).
% 2.04/2.24 tff(4954,plain,
% 2.04/2.24 (~r(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[4281, 4953, 4907, 95, 4905, 94])).
% 2.04/2.24 tff(4955,plain,
% 2.04/2.24 (b(s(s(s(s(z)))), z)),
% 2.04/2.24 inference(unit_resolution,[status(thm)],[274, 4954])).
% 2.04/2.24 tff(4956,plain,
% 2.04/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4957,plain,
% 2.04/2.25 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4958,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4957])).
% 2.04/2.25 tff(4959,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4958, 4956])).
% 2.04/2.25 tff(4960,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4961,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4960, 4959])).
% 2.04/2.25 tff(4962,plain,
% 2.04/2.25 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4961, 171, 3137, 4951, 4903, 4955])).
% 2.04/2.25 tff(4963,plain,
% 2.04/2.25 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[498, 4962])).
% 2.04/2.25 tff(4964,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4072, 4963, 126, 94])).
% 2.04/2.25 tff(4965,plain,
% 2.04/2.25 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[225, 4964])).
% 2.04/2.25 tff(4966,plain,
% 2.04/2.25 (~r(s(z), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4947, 2116, 126, 83, 84, 3137, 95, 600])).
% 2.04/2.25 tff(4967,plain,
% 2.04/2.25 (b(s(z), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[550, 4966])).
% 2.04/2.25 tff(4968,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[544, 4967, 4905, 83, 126, 94, 95])).
% 2.04/2.25 tff(4969,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3668, 4968])).
% 2.04/2.25 tff(4970,plain,
% 2.04/2.25 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3713, 4969, 94, 95, 4905, 4967, 4903])).
% 2.04/2.25 tff(4971,plain,
% 2.04/2.25 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[205, 4970])).
% 2.04/2.25 tff(4972,plain,
% 2.04/2.25 (~r(s(s(s(s(z)))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4281, 4971, 600, 95, 4905, 94])).
% 2.04/2.25 tff(4973,plain,
% 2.04/2.25 (b(s(s(s(s(z)))), z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[274, 4972])).
% 2.04/2.25 tff(4974,plain,
% 2.04/2.25 (~b(z, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4961, 171, 3137, 4969, 4903, 4973])).
% 2.04/2.25 tff(4975,plain,
% 2.04/2.25 (r(z, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[498, 4974])).
% 2.04/2.25 tff(4976,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4072, 4975, 126, 94])).
% 2.04/2.25 tff(4977,plain,
% 2.04/2.25 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[671])).
% 2.04/2.25 tff(4978,plain,
% 2.04/2.25 (~(elem!1 = s(z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4919, 4977])).
% 2.04/2.25 tff(4979,plain,
% 2.04/2.25 (b(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[687, 676, 4978])).
% 2.04/2.25 tff(4980,plain,
% 2.04/2.25 (~b(elem!1, s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3733, 171, 323, 4979, 259])).
% 2.04/2.25 tff(4981,plain,
% 2.04/2.25 (r(elem!1, s(s(z)))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3154, 4980, 3738])).
% 2.04/2.25 tff(4982,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4983,plain,
% 2.04/2.25 (((~r(z, s(z))) | (~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(z, s(z))) | (~r(s(s(z)), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4984,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4983])).
% 2.04/2.25 tff(4985,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4984, 4982])).
% 2.04/2.25 tff(4986,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4987,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4986, 4985])).
% 2.04/2.25 tff(4988,plain,
% 2.04/2.25 ((~r(elem!1, z)) | (~r(elem!1, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4987, 106])).
% 2.04/2.25 tff(4989,plain,
% 2.04/2.25 (~r(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4988, 4981, 94, 637])).
% 2.04/2.25 tff(4990,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1567, 4989, 1553])).
% 2.04/2.25 tff(4991,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4992,plain,
% 2.04/2.25 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(4993,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[4992])).
% 2.04/2.25 tff(4994,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[4993, 4991])).
% 2.04/2.25 tff(4995,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(4996,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[4995, 4994])).
% 2.04/2.25 tff(4997,plain,
% 2.04/2.25 ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4996, 171, 3137, 4979, 159])).
% 2.04/2.25 tff(4998,plain,
% 2.04/2.25 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4997, 4990])).
% 2.04/2.25 tff(4999,plain,
% 2.04/2.25 (~b(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4060, 4979, 259, 323])).
% 2.04/2.25 tff(5000,plain,
% 2.04/2.25 (r(s(s(z)), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1416, 4999, 2116])).
% 2.04/2.25 tff(5001,plain,
% 2.04/2.25 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[3449, 4981, 219])).
% 2.04/2.25 tff(5002,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5003,plain,
% 2.04/2.25 (((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5004,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5003])).
% 2.04/2.25 tff(5005,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5004, 5002])).
% 2.04/2.25 tff(5006,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5007,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5006, 5005])).
% 2.04/2.25 tff(5008,plain,
% 2.04/2.25 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5007, 171, 3137, 4990, 159])).
% 2.04/2.25 tff(5009,plain,
% 2.04/2.25 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[782, 5008, 5001])).
% 2.04/2.25 tff(5010,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5011,plain,
% 2.04/2.25 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5012,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5011])).
% 2.04/2.25 tff(5013,plain,
% 2.04/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5012, 5010])).
% 2.04/2.25 tff(5014,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5015,plain,
% 2.04/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5014, 5013])).
% 2.04/2.25 tff(5016,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5015, 106, 1403, 769, 2027, 501])).
% 2.04/2.25 tff(5017,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5018,plain,
% 2.04/2.25 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5017, 5009, 501, 5000])).
% 2.04/2.25 tff(5019,plain,
% 2.04/2.25 (s(s(s(s(s(z))))) = elem!1),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[853, 5018, 4998])).
% 2.04/2.25 tff(5020,plain,
% 2.04/2.25 (elem!1 = s(s(s(s(s(z)))))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5019, 759])).
% 2.04/2.25 tff(5021,plain,
% 2.04/2.25 ($false),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5001, 5020])).
% 2.04/2.25 tff(5022,plain,(r(elem!1, s(z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | r(s(s(s(s(s(z))))), s(s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (s(s(z)) = elem!1) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.25 tff(5023,plain,
% 2.04/2.25 (r(elem!1, s(z))),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5022, 637, 3137, 4903, 4971, 4976, 4967, 4905, 2116, 84])).
% 2.04/2.25 tff(5024,plain,
% 2.04/2.25 (~r(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4937, 5023, 94, 95])).
% 2.04/2.25 tff(5025,plain,
% 2.04/2.25 (~(z = elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[4432, 5023, 600, 83, 4905, 4967, 95, 4969, 126, 94])).
% 2.04/2.25 tff(5026,plain,
% 2.04/2.25 (~(elem!1 = z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[697, 5025])).
% 2.04/2.25 tff(5027,plain,
% 2.04/2.25 (b(elem!1, z)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[1567, 5026, 5024])).
% 2.04/2.25 tff(5028,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5029,plain,
% 2.04/2.25 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(rewrite,[status(thm)],[])).
% 2.04/2.25 tff(5030,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.25 inference(monotonicity,[status(thm)],[5029])).
% 2.04/2.25 tff(5031,plain,
% 2.04/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.25 inference(transitivity,[status(thm)],[5030, 5028])).
% 2.04/2.25 tff(5032,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.25 inference(quant_inst,[status(thm)],[])).
% 2.04/2.25 tff(5033,plain,
% 2.04/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.25 inference(modus_ponens,[status(thm)],[5032, 5031])).
% 2.04/2.25 tff(5034,plain,
% 2.04/2.25 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.25 inference(unit_resolution,[status(thm)],[5033, 171, 3137, 5027, 4903])).
% 2.04/2.26 tff(5035,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1296, 4975, 126, 95])).
% 2.04/2.26 tff(5036,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1305, 5035, 3829])).
% 2.04/2.26 tff(5037,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 2.04/2.26 tff(5038,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5037])).
% 2.04/2.26 tff(5039,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.26 inference(symmetry,[status(thm)],[5038])).
% 2.04/2.26 tff(5040,plain,
% 2.04/2.26 ((~b(s(s(s(s(s(z))))), elem!1)) <=> (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5039])).
% 2.04/2.26 tff(5041,assumption,(~b(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 2.04/2.26 tff(5042,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5041, 5040])).
% 2.04/2.26 tff(5043,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[2010, 5042])).
% 2.04/2.26 tff(5044,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | b(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5045,plain,
% 2.04/2.26 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5044, 5034, 5036])).
% 2.04/2.26 tff(5046,plain,
% 2.04/2.26 (~r(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[4144, 1016, 259, 96, 95])).
% 2.04/2.26 tff(5047,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1578, 25, 724, 5046])).
% 2.04/2.26 tff(5048,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3859, 25, 4472, 3931])).
% 2.04/2.26 tff(5049,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5050,plain,
% 2.04/2.26 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5051,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5050])).
% 2.04/2.26 tff(5052,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5051, 5049])).
% 2.04/2.26 tff(5053,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5054,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5053, 5052])).
% 2.04/2.26 tff(5055,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5054, 171, 3137, 1596, 5048, 5047])).
% 2.04/2.26 tff(5056,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5057,plain,
% 2.04/2.26 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5056, 5045, 3137, 5023, 5027, 4967, 4905, 94, 95])).
% 2.04/2.26 tff(5058,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1013, 5057])).
% 2.04/2.26 tff(5059,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5060,plain,
% 2.04/2.26 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5061,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5060])).
% 2.04/2.26 tff(5062,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5061, 5059])).
% 2.04/2.26 tff(5063,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5064,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5063, 5062])).
% 2.04/2.26 tff(5065,plain,
% 2.04/2.26 (~r(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5064, 106, 991, 637, 600])).
% 2.04/2.26 tff(5066,plain,
% 2.04/2.26 (b(s(s(s(elem!1))), z)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1578, 25, 724, 5065])).
% 2.04/2.26 tff(5067,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5068,plain,
% 2.04/2.26 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5069,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5068])).
% 2.04/2.26 tff(5070,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5069, 5067])).
% 2.04/2.26 tff(5071,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5072,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 2.04/2.26 tff(5073,plain,
% 2.04/2.26 (~r(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5072, 106, 991, 637, 600])).
% 2.04/2.26 tff(5074,plain,
% 2.04/2.26 (b(z, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[1593, 25, 5073, 3930])).
% 2.04/2.26 tff(5075,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3354, 171, 1596, 5074, 5066])).
% 2.04/2.26 tff(5076,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5077,plain,
% 2.04/2.26 (((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5078,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1)))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5077])).
% 2.04/2.26 tff(5079,plain,
% 2.04/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1))))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5078, 5076])).
% 2.04/2.26 tff(5080,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, s(s(s(elem!1))))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5081,plain,
% 2.04/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(elem!1)))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5080, 5079])).
% 2.04/2.26 tff(5082,plain,
% 2.04/2.26 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5081, 171, 1596, 5074, 5066])).
% 2.04/2.26 tff(5083,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5084,plain,
% 2.04/2.26 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5085,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5084])).
% 2.04/2.26 tff(5086,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5085, 5083])).
% 2.04/2.26 tff(5087,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5088,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5087, 5086])).
% 2.04/2.26 tff(5089,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5088, 106, 730, 95, 502])).
% 2.04/2.26 tff(5090,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5033, 171, 3137, 1596, 4672])).
% 2.04/2.26 tff(5091,plain,
% 2.04/2.26 (s(s(s(s(s(z))))) = elem!1),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[853, 5090, 5089])).
% 2.04/2.26 tff(5092,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5091])).
% 2.04/2.26 tff(5093,plain,
% 2.04/2.26 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.04/2.26 inference(transitivity,[status(thm)],[5092, 3511])).
% 2.04/2.26 tff(5094,plain,
% 2.04/2.26 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5093])).
% 2.04/2.26 tff(5095,plain,
% 2.04/2.26 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5007, 171, 3137, 1596, 4672])).
% 2.04/2.26 tff(5096,plain,
% 2.04/2.26 (elem!1 = s(s(s(s(s(z)))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[782, 5095, 778])).
% 2.04/2.26 tff(5097,plain,
% 2.04/2.26 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3279, 5096])).
% 2.04/2.26 tff(5098,plain,
% 2.04/2.26 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5097, 5094])).
% 2.04/2.26 tff(5099,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 2.04/2.26 tff(5100,plain,
% 2.04/2.26 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3859, 25, 5099])).
% 2.04/2.26 tff(5101,plain,
% 2.04/2.26 (r(s(s(s(elem!1))), elem!1)),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5100, 5098])).
% 2.04/2.26 tff(5102,plain,
% 2.04/2.26 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[3301, 5096, 934, 5097])).
% 2.04/2.26 tff(5103,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5104,plain,
% 2.04/2.26 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(rewrite,[status(thm)],[])).
% 2.04/2.26 tff(5105,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.04/2.26 inference(monotonicity,[status(thm)],[5104])).
% 2.04/2.26 tff(5106,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(transitivity,[status(thm)],[5105, 5103])).
% 2.04/2.26 tff(5107,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.26 inference(quant_inst,[status(thm)],[])).
% 2.04/2.26 tff(5108,plain,
% 2.04/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.26 inference(modus_ponens,[status(thm)],[5107, 5106])).
% 2.04/2.26 tff(5109,plain,
% 2.04/2.26 ($false),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5108, 106, 5102, 5101, 991, 1403])).
% 2.04/2.26 tff(5110,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | b(s(s(s(elem!1))), elem!1) | b(elem!1, s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.26 tff(5111,plain,
% 2.04/2.26 (~r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[5110, 5082, 1403, 991, 5075, 3137, 1596, 96, 95, 730])).
% 2.04/2.26 tff(5112,plain,
% 2.04/2.26 (b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[479, 5111])).
% 2.04/2.26 tff(5113,plain,
% 2.04/2.26 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[471, 171, 866, 259, 5112])).
% 2.04/2.26 tff(5114,plain,
% 2.04/2.26 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.26 inference(unit_resolution,[status(thm)],[225, 5113])).
% 2.04/2.26 tff(5115,plain,
% 2.04/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5116,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5117,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5116, 5115])).
% 2.04/2.27 tff(5118,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5117, 106, 991, 637, 5114])).
% 2.04/2.27 tff(5119,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1305, 5118, 1300])).
% 2.04/2.27 tff(5120,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[959, 5114, 637, 96])).
% 2.04/2.27 tff(5121,plain,
% 2.04/2.27 (b(s(s(s(s(s(z))))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[143, 25, 140, 5120])).
% 2.04/2.27 tff(5122,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5123,plain,
% 2.04/2.27 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5124,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5123])).
% 2.04/2.27 tff(5125,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5124, 5122])).
% 2.04/2.27 tff(5126,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5127,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5126, 5125])).
% 2.04/2.27 tff(5128,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5127, 171, 3137, 5074, 5066, 5121, 5119])).
% 2.04/2.27 tff(5129,plain,((~r(z, s(s(z)))) | (~b(z, elem!1)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~b(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5130,plain,
% 2.04/2.27 (~r(s(s(z)), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5129, 5058, 94, 3137, 3829, 600, 4905, 637, 5023, 95, 5027])).
% 2.04/2.27 tff(5131,plain,
% 2.04/2.27 (b(s(s(z)), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1416, 5130, 2116])).
% 2.04/2.27 tff(5132,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5133,plain,
% 2.04/2.27 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5134,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5133])).
% 2.04/2.27 tff(5135,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5134, 5132])).
% 2.04/2.27 tff(5136,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5137,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5136, 5135])).
% 2.04/2.27 tff(5138,plain,
% 2.04/2.27 ((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5137, 171])).
% 2.04/2.27 tff(5139,plain,
% 2.04/2.27 (~b(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5138, 5131, 3137, 5027, 4905])).
% 2.04/2.27 tff(5140,plain,
% 2.04/2.27 (r(s(z), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1444, 5139, 4919])).
% 2.04/2.27 tff(5141,plain,
% 2.04/2.27 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[2035, 5140, 5023, 126])).
% 2.04/2.27 tff(5142,plain,
% 2.04/2.27 (s(s(s(s(s(z))))) = elem!1),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[853, 5141, 5034])).
% 2.04/2.27 tff(5143,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(s(s(z)), elem!1)),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5142])).
% 2.04/2.27 tff(5144,plain,
% 2.04/2.27 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(symmetry,[status(thm)],[5143])).
% 2.04/2.27 tff(5145,plain,
% 2.04/2.27 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5131, 5144])).
% 2.04/2.27 tff(5146,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4970, 5145])).
% 2.04/2.27 tff(5147,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (s(s(z)) = elem!1) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5148,plain,
% 2.04/2.27 (~r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5147, 4911, 3137, 126, 4907, 95, 83, 84])).
% 2.04/2.27 tff(5149,plain,
% 2.04/2.27 (b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[157, 5148])).
% 2.04/2.27 tff(5150,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5151,plain,
% 2.04/2.27 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5152,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5151])).
% 2.04/2.27 tff(5153,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5152, 5150])).
% 2.04/2.27 tff(5154,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5155,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5154, 5153])).
% 2.04/2.27 tff(5156,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5155, 171, 3137, 679, 259, 1, 207, 159])).
% 2.04/2.27 tff(5157,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5158,plain,
% 2.04/2.27 (~b(elem!1, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5157, 5149, 4905, 3137, 4965, 4903])).
% 2.04/2.27 tff(5159,plain,
% 2.04/2.27 (r(elem!1, s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[687, 5158, 4978])).
% 2.04/2.27 tff(5160,plain,
% 2.04/2.27 (~r(elem!1, z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4937, 5159, 94, 95])).
% 2.04/2.27 tff(5161,plain,
% 2.04/2.27 (~(z = elem!1)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4432, 5159, 4907, 83, 4905, 4949, 95, 4951, 126, 94])).
% 2.04/2.27 tff(5162,plain,
% 2.04/2.27 (~(elem!1 = z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[697, 5161])).
% 2.04/2.27 tff(5163,plain,
% 2.04/2.27 (b(elem!1, z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[1567, 5162, 5160])).
% 2.04/2.27 tff(5164,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5165,plain,
% 2.04/2.27 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5166,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5165])).
% 2.04/2.27 tff(5167,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5166, 5164])).
% 2.04/2.27 tff(5168,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5169,plain,
% 2.04/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5168, 5167])).
% 2.04/2.27 tff(5170,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5169, 171, 3137, 5163, 5149, 4965, 4903])).
% 2.04/2.27 tff(5171,plain,(b(z, s(s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5172,plain,
% 2.04/2.27 (b(z, s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5171, 4901, 83, 31, 61, 84])).
% 2.04/2.27 tff(5173,plain,
% 2.04/2.27 (~r(s(s(z)), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[234, 96, 126, 95])).
% 2.04/2.27 tff(5174,plain,
% 2.04/2.27 (b(s(s(z)), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[244, 5173])).
% 2.04/2.27 tff(5175,plain,
% 2.04/2.27 (~b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[179, 160, 146, 161])).
% 2.04/2.27 tff(5176,plain,
% 2.04/2.27 (r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[157, 5175])).
% 2.04/2.27 tff(5177,plain,
% 2.04/2.27 (~r(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[864, 106, 96, 5176, 95])).
% 2.04/2.27 tff(5178,plain,
% 2.04/2.27 (b(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[550, 5177])).
% 2.04/2.27 tff(5179,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[544, 5178, 5174, 83, 126, 96, 95])).
% 2.04/2.27 tff(5180,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3713, 5178, 96, 95, 5174, 160, 146])).
% 2.04/2.27 tff(5181,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3668, 5180, 5179])).
% 2.04/2.27 tff(5182,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5183,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5182, 94, 31, 83, 61, 5172])).
% 2.04/2.27 tff(5184,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[205, 5183])).
% 2.04/2.27 tff(5185,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[864, 106, 554, 96, 637, 95])).
% 2.04/2.27 tff(5186,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5187,plain,
% 2.04/2.27 (~r(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5186, 554, 96, 95])).
% 2.04/2.27 tff(5188,plain,
% 2.04/2.27 (b(s(s(z)), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[157, 5187])).
% 2.04/2.27 tff(5189,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[215, 5188, 146, 161])).
% 2.04/2.27 tff(5190,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[225, 5189])).
% 2.04/2.27 tff(5191,plain,
% 2.04/2.27 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5192,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.04/2.27 inference(monotonicity,[status(thm)],[5191])).
% 2.04/2.27 tff(5193,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.04/2.27 inference(transitivity,[status(thm)],[5192, 4613])).
% 2.04/2.27 tff(5194,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5195,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5194, 5193])).
% 2.04/2.27 tff(5196,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5195, 106, 554, 126, 5190, 501])).
% 2.04/2.27 tff(5197,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5198,plain,
% 2.04/2.27 (~r(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5197, 5184, 61, 5172, 94, 31])).
% 2.04/2.27 tff(5199,plain,
% 2.04/2.27 (b(s(z), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[550, 5198])).
% 2.04/2.27 tff(5200,plain,
% 2.04/2.27 ($false),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4265, 171, 323, 259, 161, 207, 159])).
% 2.04/2.27 tff(5201,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.27 tff(5202,plain,
% 2.04/2.27 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5201, 5199, 245, 5172, 257])).
% 2.04/2.27 tff(5203,plain,
% 2.04/2.27 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[225, 5202])).
% 2.04/2.27 tff(5204,plain,
% 2.04/2.27 (~r(z, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4072, 5203, 61, 94])).
% 2.04/2.27 tff(5205,plain,
% 2.04/2.27 (b(z, s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[498, 5204])).
% 2.04/2.27 tff(5206,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[544, 5199, 245, 83, 61, 94, 31])).
% 2.04/2.27 tff(5207,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[3668, 5206])).
% 2.04/2.27 tff(5208,plain,
% 2.04/2.27 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4961, 171, 4901, 5207, 257])).
% 2.04/2.27 tff(5209,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5208, 5205])).
% 2.04/2.27 tff(5210,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), z)),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[274, 5209])).
% 2.04/2.27 tff(5211,plain,
% 2.04/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.27 inference(rewrite,[status(thm)],[])).
% 2.04/2.27 tff(5212,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.04/2.27 inference(quant_inst,[status(thm)],[])).
% 2.04/2.27 tff(5213,plain,
% 2.04/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 2.04/2.27 inference(modus_ponens,[status(thm)],[5212, 5211])).
% 2.04/2.27 tff(5214,plain,
% 2.04/2.27 (~r(s(s(s(s(z)))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[5213, 106, 94, 31, 5210])).
% 2.04/2.27 tff(5215,plain,
% 2.04/2.27 (b(s(s(s(s(z)))), s(z))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[321, 5214, 255])).
% 2.04/2.27 tff(5216,plain,
% 2.04/2.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[329, 171, 5199, 245, 5215])).
% 2.04/2.27 tff(5217,plain,
% 2.04/2.27 (r(s(s(z)), s(s(s(s(z)))))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[351, 5216])).
% 2.04/2.27 tff(5218,plain,
% 2.04/2.27 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[4319, 5207, 245, 83, 94, 5199, 257])).
% 2.04/2.27 tff(5219,plain,
% 2.04/2.27 (r(s(s(s(s(z)))), s(s(z)))),
% 2.04/2.27 inference(unit_resolution,[status(thm)],[374, 5218, 355])).
% 2.04/2.27 tff(5220,plain,
% 2.04/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5221,plain,
% 2.04/2.28 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5222,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5221])).
% 2.04/2.28 tff(5223,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[5222, 5220])).
% 2.04/2.28 tff(5224,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(5225,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5224, 5223])).
% 2.04/2.28 tff(5226,plain,
% 2.04/2.28 (~b(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5225, 171, 5199, 5172, 83, 257, 5215])).
% 2.04/2.28 tff(5227,plain,
% 2.04/2.28 (r(z, s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[293, 5226])).
% 2.04/2.28 tff(5228,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5229,plain,
% 2.04/2.28 (((~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)))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5230,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5229])).
% 2.04/2.28 tff(5231,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[5230, 5228])).
% 2.04/2.28 tff(5232,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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)))))) | (~r(s(s(z)), z)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(5233,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5232, 5231])).
% 2.04/2.28 tff(5234,plain,
% 2.04/2.28 (~r(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5233, 106, 5227, 5219, 5217])).
% 2.04/2.28 tff(5235,plain,
% 2.04/2.28 (b(s(s(z)), z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[157, 5234])).
% 2.04/2.28 tff(5236,plain,
% 2.04/2.28 (~(s(z) = elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4918, 84, 4901])).
% 2.04/2.28 tff(5237,plain,
% 2.04/2.28 (~r(s(z), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[2136, 106, 94, 31, 5210])).
% 2.04/2.28 tff(5238,plain,
% 2.04/2.28 (b(s(z), s(s(s(s(z)))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[454, 5237, 254])).
% 2.04/2.28 tff(5239,plain,
% 2.04/2.28 (~b(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[445, 5238, 245, 5215])).
% 2.04/2.28 tff(5240,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5241,plain,
% 2.04/2.28 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5242,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5241])).
% 2.04/2.28 tff(5243,plain,
% 2.04/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[5242, 5240])).
% 2.04/2.28 tff(5244,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(5245,plain,
% 2.04/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5244, 5243])).
% 2.04/2.28 tff(5246,plain,
% 2.04/2.28 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5245, 171, 3137, 4979, 83, 357, 1313])).
% 2.04/2.28 tff(5247,assumption,(~b(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.04/2.28 tff(5248,plain,
% 2.04/2.28 ((~b(s(s(s(s(s(z))))), s(z))) <=> (~b(elem!1, s(z)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[4817])).
% 2.04/2.28 tff(5249,plain,
% 2.04/2.28 (~b(elem!1, s(z))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5247, 5248])).
% 2.04/2.28 tff(5250,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[679, 5249])).
% 2.04/2.28 tff(5251,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(5252,plain,
% 2.04/2.28 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5251, 4979, 5247])).
% 2.04/2.28 tff(5253,plain,
% 2.04/2.28 (r(elem!1, s(s(s(s(s(z))))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[782, 5252, 5246])).
% 2.04/2.28 tff(5254,plain,
% 2.04/2.28 (~r(s(s(z)), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3767, 5253, 501, 396])).
% 2.04/2.28 tff(5255,plain,
% 2.04/2.28 (s(s(z)) = elem!1),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1416, 5254, 4999])).
% 2.04/2.28 tff(5256,plain,
% 2.04/2.28 (s(s(s(z))) = s(elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5255])).
% 2.04/2.28 tff(5257,plain,
% 2.04/2.28 (s(elem!1) = s(s(s(z)))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5256])).
% 2.04/2.28 tff(5258,plain,
% 2.04/2.28 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5256])).
% 2.04/2.28 tff(5259,plain,
% 2.04/2.28 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5258])).
% 2.04/2.28 tff(5260,plain,
% 2.04/2.28 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5259, 5257])).
% 2.04/2.28 tff(5261,plain,
% 2.04/2.28 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[5260, 1125])).
% 2.04/2.28 tff(5262,plain,
% 2.04/2.28 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(elem!1))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5261])).
% 2.04/2.28 tff(5263,plain,
% 2.04/2.28 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5262])).
% 2.04/2.28 tff(5264,plain,
% 2.04/2.28 (~(s(s(elem!1)) = s(elem!1))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[2264, 5263])).
% 2.04/2.28 tff(5265,plain,
% 2.04/2.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5259])).
% 2.04/2.28 tff(5266,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(symmetry,[status(thm)],[5265])).
% 2.04/2.28 tff(5267,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(z)))), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5255])).
% 2.04/2.28 tff(5268,plain,
% 2.04/2.28 (r(s(s(s(s(z)))), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[569, 5267])).
% 2.04/2.28 tff(5269,plain,
% 2.04/2.28 (r(s(s(elem!1)), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5268, 5266])).
% 2.04/2.28 tff(5270,plain,
% 2.04/2.28 (~(s(elem!1) = elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1492, 5255])).
% 2.04/2.28 tff(5271,plain,
% 2.04/2.28 (b(s(z), s(s(z))) <=> b(s(z), elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5255])).
% 2.04/2.28 tff(5272,plain,
% 2.04/2.28 (b(s(z), elem!1)),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[323, 5271])).
% 2.04/2.28 tff(5273,plain,
% 2.04/2.28 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1613, 5255, 1535])).
% 2.04/2.28 tff(5274,plain,
% 2.04/2.28 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1620, 5273])).
% 2.04/2.28 tff(5275,plain,
% 2.04/2.28 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5258])).
% 2.04/2.28 tff(5276,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5275])).
% 2.04/2.28 tff(5277,plain,
% 2.04/2.28 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[479, 5247])).
% 2.04/2.28 tff(5278,plain,
% 2.04/2.28 (r(s(s(s(elem!1))), s(z))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5277, 5276])).
% 2.04/2.28 tff(5279,plain,
% 2.04/2.28 (~r(s(elem!1), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1712, 5278, 95, 94, 5274])).
% 2.04/2.28 tff(5280,plain,
% 2.04/2.28 (b(s(elem!1), s(z))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1717, 5279, 1535])).
% 2.04/2.28 tff(5281,plain,
% 2.04/2.28 (~r(elem!1, z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[4002, 5255, 152])).
% 2.04/2.28 tff(5282,plain,
% 2.04/2.28 (b(elem!1, z)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1567, 5281, 1553])).
% 2.04/2.28 tff(5283,plain,
% 2.04/2.28 (~b(s(elem!1), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1724, 171, 5282, 4979, 5280, 5272])).
% 2.04/2.28 tff(5284,plain,
% 2.04/2.28 (r(s(elem!1), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1523, 5283, 5270])).
% 2.04/2.28 tff(5285,plain,
% 2.04/2.28 (r(elem!1, s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[3887, 5255, 501])).
% 2.04/2.28 tff(5286,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5287,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(5288,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5287, 5286])).
% 2.04/2.28 tff(5289,plain,
% 2.04/2.28 (~r(s(s(elem!1)), s(elem!1))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5288, 106, 5285, 5284, 5269])).
% 2.04/2.28 tff(5290,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.28 tff(5291,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5292,plain,
% 2.04/2.28 (((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~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(s(s(elem!1))), s(z))))),
% 2.04/2.28 inference(rewrite,[status(thm)],[])).
% 2.04/2.28 tff(5293,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5292])).
% 2.04/2.28 tff(5294,plain,
% 2.04/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.04/2.28 inference(transitivity,[status(thm)],[5293, 5291])).
% 2.04/2.28 tff(5295,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 2.04/2.28 inference(quant_inst,[status(thm)],[])).
% 2.04/2.28 tff(5296,plain,
% 2.04/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(z)))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5295, 5294])).
% 2.04/2.28 tff(5297,plain,
% 2.04/2.28 (~r(s(elem!1), elem!1)),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5296, 106, 1652, 5290, 1571])).
% 2.04/2.28 tff(5298,plain,
% 2.04/2.28 (s(elem!1) = elem!1),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1523, 5297, 1518])).
% 2.04/2.28 tff(5299,plain,
% 2.04/2.28 (s(s(elem!1)) = s(elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5298])).
% 2.04/2.28 tff(5300,plain,
% 2.04/2.28 (s(s(elem!1)) = elem!1),
% 2.04/2.28 inference(transitivity,[status(thm)],[5299, 5298])).
% 2.04/2.28 tff(5301,plain,
% 2.04/2.28 (s(s(s(elem!1))) = s(elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5300])).
% 2.04/2.28 tff(5302,plain,
% 2.04/2.28 (s(s(s(elem!1))) = elem!1),
% 2.04/2.28 inference(transitivity,[status(thm)],[5301, 5298])).
% 2.04/2.28 tff(5303,plain,
% 2.04/2.28 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, elem!1)),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5302])).
% 2.04/2.28 tff(5304,plain,
% 2.04/2.28 (r(elem!1, elem!1) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5303])).
% 2.04/2.28 tff(5305,plain,
% 2.04/2.28 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5304])).
% 2.04/2.28 tff(5306,plain,
% 2.04/2.28 (~r(elem!1, s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[3996, 5305])).
% 2.04/2.28 tff(5307,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1652, 5306])).
% 2.04/2.28 tff(5308,plain,((~r(elem!1, s(s(s(elem!1))))) | b(s(elem!1), elem!1) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.28 tff(5309,plain,
% 2.04/2.28 (~r(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5308, 5283, 5285, 5278])).
% 2.04/2.28 tff(5310,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.28 tff(5311,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.28 tff(5312,plain,
% 2.04/2.28 ($false),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[1703, 25, 5311, 1693, 5310])).
% 2.04/2.28 tff(5313,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,[]))).
% 2.04/2.28 tff(5314,plain,
% 2.04/2.28 (b(s(elem!1), s(s(s(elem!1))))),
% 2.04/2.28 inference(unit_resolution,[status(thm)],[5313, 5309, 5274])).
% 2.04/2.28 tff(5315,plain,
% 2.04/2.28 (s(s(s(elem!1))) = s(s(s(s(s(z)))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5275])).
% 2.04/2.28 tff(5316,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5315])).
% 2.04/2.28 tff(5317,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.28 inference(symmetry,[status(thm)],[5316])).
% 2.04/2.28 tff(5318,plain,
% 2.04/2.28 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(monotonicity,[status(thm)],[5258])).
% 2.04/2.28 tff(5319,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[3686, 5318])).
% 2.04/2.28 tff(5320,plain,
% 2.04/2.28 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.04/2.28 inference(modus_ponens,[status(thm)],[5319, 5317])).
% 2.04/2.28 tff(5321,plain,
% 2.04/2.29 (r(s(s(z)), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5255])).
% 2.04/2.29 tff(5322,plain,
% 2.04/2.29 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[5321])).
% 2.04/2.29 tff(5323,plain,
% 2.04/2.29 (r(s(s(z)), s(s(s(elem!1))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5285, 5322])).
% 2.04/2.29 tff(5324,plain,
% 2.04/2.29 (b(s(s(z)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[157, 152])).
% 2.04/2.29 tff(5325,plain,
% 2.04/2.29 (~(s(s(z)) = s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1551, 4978])).
% 2.04/2.29 tff(5326,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1778, 5280, 323, 5325, 5324, 5323, 259])).
% 2.04/2.29 tff(5327,plain,
% 2.04/2.29 (b(s(s(s(elem!1))), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1783, 5326, 5273])).
% 2.04/2.29 tff(5328,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5329,plain,
% 2.04/2.29 (((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5330,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5329])).
% 2.04/2.29 tff(5331,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5330, 5328])).
% 2.04/2.29 tff(5332,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5333,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 2.04/2.29 tff(5334,plain,
% 2.04/2.29 ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5333, 171, 5327, 5280, 5320])).
% 2.04/2.29 tff(5335,plain,
% 2.04/2.29 (~b(s(s(elem!1)), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5334, 5314])).
% 2.04/2.29 tff(5336,plain,
% 2.04/2.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5337,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5338,plain,
% 2.04/2.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5337, 5336])).
% 2.04/2.29 tff(5339,plain,
% 2.04/2.29 ((s(s(elem!1)) = s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5338, 25, 5335])).
% 2.04/2.29 tff(5340,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5339, 5289, 5264])).
% 2.04/2.29 tff(5341,plain,(r(elem!1, s(z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | r(s(s(z)), z) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | b(s(s(s(s(s(z))))), s(z)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(5342,plain,
% 2.04/2.29 (r(elem!1, s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5341, 5199, 245, 31, 5207, 5219, 5234, 5184, 5203, 5239, 4901, 83, 5215, 5205, 84])).
% 2.04/2.29 tff(5343,plain,
% 2.04/2.29 (r(s(s(s(s(s(z))))), s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[479, 5239])).
% 2.04/2.29 tff(5344,plain,
% 2.04/2.29 (elem!1 = z),
% 2.04/2.29 inference(transitivity,[status(thm)],[1548, 917, 44])).
% 2.04/2.29 tff(5345,plain,
% 2.04/2.29 (b(z, elem!1) <=> b(z, z)),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5344])).
% 2.04/2.29 tff(5346,plain,
% 2.04/2.29 (b(z, z) <=> b(z, elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[5345])).
% 2.04/2.29 tff(5347,plain,
% 2.04/2.29 ((~b(z, z)) <=> (~b(z, elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5346])).
% 2.04/2.29 tff(5348,plain,
% 2.04/2.29 ((~![X: $i] : (~b(X, X))) | (~b(z, z))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5349,plain,
% 2.04/2.29 (~b(z, z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5348, 2097])).
% 2.04/2.29 tff(5350,plain,
% 2.04/2.29 (~b(z, elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5349, 5347])).
% 2.04/2.29 tff(5351,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3137, 5350])).
% 2.04/2.29 tff(5352,plain,((~(s(elem!1) = s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(5353,plain,
% 2.04/2.29 (~(s(elem!1) = s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5352, 4901])).
% 2.04/2.29 tff(5354,plain,
% 2.04/2.29 (~(z = elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[703, 5353])).
% 2.04/2.29 tff(5355,plain,
% 2.04/2.29 (~r(elem!1, z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[4937, 730, 96, 95])).
% 2.04/2.29 tff(5356,plain,
% 2.04/2.29 (b(elem!1, z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1567, 3218, 5355])).
% 2.04/2.29 tff(5357,plain,
% 2.04/2.29 (~b(s(s(z)), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3227, 5356, 3137, 1])).
% 2.04/2.29 tff(5358,plain,
% 2.04/2.29 (~(s(elem!1) = s(z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[922, 695])).
% 2.04/2.29 tff(5359,plain,
% 2.04/2.29 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[2184, 5358])).
% 2.04/2.29 tff(5360,plain,
% 2.04/2.29 (elem!1 = s(s(s(s(s(z)))))),
% 2.04/2.29 inference(symmetry,[status(thm)],[5091])).
% 2.04/2.29 tff(5361,plain,
% 2.04/2.29 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5360])).
% 2.04/2.29 tff(5362,plain,
% 2.04/2.29 ((s(s(s(z))) = s(s(s(s(s(z)))))) <=> (s(s(s(z))) = elem!1)),
% 2.04/2.29 inference(symmetry,[status(thm)],[5361])).
% 2.04/2.29 tff(5363,plain,
% 2.04/2.29 ((~(s(s(s(z))) = s(s(s(s(s(z))))))) <=> (~(s(s(s(z))) = elem!1))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5362])).
% 2.04/2.29 tff(5364,plain,
% 2.04/2.29 (~(s(s(s(z))) = s(s(s(s(s(z))))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3095, 5096])).
% 2.04/2.29 tff(5365,plain,
% 2.04/2.29 (~(s(s(s(z))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5364, 5363])).
% 2.04/2.29 tff(5366,assumption,(~(s(s(s(z))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.04/2.29 tff(5367,plain,
% 2.04/2.29 (~(s(s(s(elem!1))) = elem!1)),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[1300, 5094])).
% 2.04/2.29 tff(5368,plain,
% 2.04/2.29 (~r(z, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1411, 554, 96, 1403])).
% 2.04/2.29 tff(5369,plain,
% 2.04/2.29 (b(z, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[124, 5368])).
% 2.04/2.29 tff(5370,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5371,plain,
% 2.04/2.29 (((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5372,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5371])).
% 2.04/2.29 tff(5373,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5372, 5370])).
% 2.04/2.29 tff(5374,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, elem!1)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5375,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 2.04/2.29 tff(5376,plain,
% 2.04/2.29 ((~b(z, elem!1)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5375, 171])).
% 2.04/2.29 tff(5377,plain,
% 2.04/2.29 (~b(elem!1, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5376, 5369, 3137, 1])).
% 2.04/2.29 tff(5378,plain,
% 2.04/2.29 (r(elem!1, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3154, 5377, 3122])).
% 2.04/2.29 tff(5379,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5380,plain,
% 2.04/2.29 (((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5381,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5380])).
% 2.04/2.29 tff(5382,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5381, 5379])).
% 2.04/2.29 tff(5383,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(z))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5384,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5383, 5382])).
% 2.04/2.29 tff(5385,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5384, 106, 554, 730, 5378, 1403])).
% 2.04/2.29 tff(5386,plain,((~r(s(z), s(s(z)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(z))) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(5387,plain,
% 2.04/2.29 (~b(s(s(z)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5386, 554, 1403, 3122, 3137, 730, 96])).
% 2.04/2.29 tff(5388,plain,
% 2.04/2.29 (r(s(s(z)), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[157, 5387])).
% 2.04/2.29 tff(5389,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[864, 106, 554, 96, 5388, 95])).
% 2.04/2.29 tff(5390,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(z))) | (~b(z, elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(5391,plain,
% 2.04/2.29 (~r(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5390, 1403, 95, 96, 3122, 3137, 730])).
% 2.04/2.29 tff(5392,plain,
% 2.04/2.29 (b(s(z), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[550, 5391])).
% 2.04/2.29 tff(5393,plain,
% 2.04/2.29 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5056, 5367, 1596, 3137, 730, 5392, 259, 96, 95])).
% 2.04/2.29 tff(5394,plain,
% 2.04/2.29 (r(s(s(s(elem!1))), s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1013, 5393])).
% 2.04/2.29 tff(5395,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5396,plain,
% 2.04/2.29 (((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5397,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5396])).
% 2.04/2.29 tff(5398,plain,
% 2.04/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5397, 5395])).
% 2.04/2.29 tff(5399,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5400,plain,
% 2.04/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5399, 5398])).
% 2.04/2.29 tff(5401,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5400, 106, 991, 1403, 600])).
% 2.04/2.29 tff(5402,plain,
% 2.04/2.29 (b(s(s(s(elem!1))), z)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[1578, 25, 724, 5401])).
% 2.04/2.29 tff(5403,plain,
% 2.04/2.29 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5404,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5403])).
% 2.04/2.29 tff(5405,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5404, 5049])).
% 2.04/2.29 tff(5406,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5407,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5406, 5405])).
% 2.04/2.29 tff(5408,plain,
% 2.04/2.29 (~b(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5407, 171, 3137, 1596, 5402])).
% 2.04/2.29 tff(5409,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5410,plain,
% 2.04/2.29 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5411,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 2.04/2.29 inference(monotonicity,[status(thm)],[5410])).
% 2.04/2.29 tff(5412,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 2.04/2.29 inference(transitivity,[status(thm)],[5411, 5409])).
% 2.04/2.29 tff(5413,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.04/2.29 inference(quant_inst,[status(thm)],[])).
% 2.04/2.29 tff(5414,plain,
% 2.04/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 2.04/2.29 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 2.04/2.29 tff(5415,plain,
% 2.04/2.29 (~b(elem!1, s(s(s(elem!1))))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5414, 171, 3137, 1596, 5402])).
% 2.04/2.29 tff(5416,plain,
% 2.04/2.29 ($false),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5110, 5415, 5408, 1403, 991, 502, 3137, 1596, 96, 95, 730])).
% 2.04/2.29 tff(5417,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.04/2.29 tff(5418,plain,
% 2.04/2.29 (~r(z, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5417, 5394, 502, 3137, 1596, 96, 95, 730, 1403])).
% 2.04/2.29 tff(5419,plain,
% 2.04/2.29 (b(z, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[124, 5418])).
% 2.04/2.29 tff(5420,plain,
% 2.04/2.29 (~b(elem!1, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[5376, 5419, 3137, 1])).
% 2.04/2.29 tff(5421,plain,
% 2.04/2.29 (r(elem!1, s(s(z)))),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3154, 5420, 3122])).
% 2.04/2.29 tff(5422,plain,
% 2.04/2.29 (~r(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3848, 106, 5394, 5421, 1403])).
% 2.04/2.29 tff(5423,plain,
% 2.04/2.29 (b(s(s(s(elem!1))), elem!1)),
% 2.04/2.29 inference(unit_resolution,[status(thm)],[3859, 25, 5422, 5367])).
% 2.04/2.29 tff(5424,plain,
% 2.04/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.04/2.29 inference(rewrite,[status(thm)],[])).
% 2.04/2.29 tff(5425,plain,
% 2.04/2.29 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~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(elem!1, z)) | (~b(z, 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))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5426,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5425])).
% 2.14/2.30 tff(5427,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5426, 5424])).
% 2.14/2.30 tff(5428,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5429,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5428, 5427])).
% 2.14/2.30 tff(5430,plain,
% 2.14/2.30 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5429, 171, 3137, 1596, 1516, 837])).
% 2.14/2.30 tff(5431,plain,
% 2.14/2.30 (((~![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)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5432,plain,
% 2.14/2.30 ((~![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)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5433,plain,
% 2.14/2.30 ((~![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))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5432, 5431])).
% 2.14/2.30 tff(5434,plain,
% 2.14/2.30 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5433, 25, 5366, 5430])).
% 2.14/2.30 tff(5435,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5436,plain,
% 2.14/2.30 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5437,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5436])).
% 2.14/2.30 tff(5438,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5437, 5435])).
% 2.14/2.30 tff(5439,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z)))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5440,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), z))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5439, 5438])).
% 2.14/2.30 tff(5441,plain,
% 2.14/2.30 (~b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5440, 171, 3137, 1596, 837])).
% 2.14/2.30 tff(5442,plain,
% 2.14/2.30 (r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[953, 25, 194, 5441])).
% 2.14/2.30 tff(5443,plain,
% 2.14/2.30 (~b(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5054, 171, 3137, 1596, 1516])).
% 2.14/2.30 tff(5444,plain,
% 2.14/2.30 (r(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1578, 25, 724, 5443])).
% 2.14/2.30 tff(5445,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5446,plain,
% 2.14/2.30 (((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5447,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5446])).
% 2.14/2.30 tff(5448,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5447, 5445])).
% 2.14/2.30 tff(5449,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5450,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 2.14/2.30 tff(5451,plain,
% 2.14/2.30 (~b(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5450, 171, 3137, 1596, 1516])).
% 2.14/2.30 tff(5452,plain,
% 2.14/2.30 (r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1593, 25, 5451, 3930])).
% 2.14/2.30 tff(5453,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5454,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5455,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5454, 5453])).
% 2.14/2.30 tff(5456,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5455, 106, 5452, 5444, 5442, 5434])).
% 2.14/2.30 tff(5457,plain,((~b(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5458,plain,
% 2.14/2.30 (~b(s(s(s(z))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5457, 5423, 3137, 1596, 5366])).
% 2.14/2.30 tff(5459,plain,
% 2.14/2.30 (r(s(s(s(z))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[804, 5458, 5365])).
% 2.14/2.30 tff(5460,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5461,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5462,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5461, 5460])).
% 2.14/2.30 tff(5463,plain,
% 2.14/2.30 ($false),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5462, 106, 730, 1403, 2049, 1199])).
% 2.14/2.30 tff(5464,plain,((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.30 tff(5465,plain,
% 2.14/2.30 (~r(s(s(s(z))), s(s(z)))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5464, 5459, 1403, 730])).
% 2.14/2.30 tff(5466,plain,
% 2.14/2.30 (~b(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5450, 171, 3137, 1596, 5423])).
% 2.14/2.30 tff(5467,plain,
% 2.14/2.30 (r(z, s(s(s(elem!1))))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1593, 25, 5466, 3930])).
% 2.14/2.30 tff(5468,plain,
% 2.14/2.30 (~b(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5054, 171, 3137, 1596, 5423])).
% 2.14/2.30 tff(5469,plain,
% 2.14/2.30 (r(s(s(s(elem!1))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1578, 25, 724, 5468])).
% 2.14/2.30 tff(5470,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5471,plain,
% 2.14/2.30 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5472,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5471])).
% 2.14/2.30 tff(5473,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5472, 5470])).
% 2.14/2.30 tff(5474,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5475,plain,
% 2.14/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5474, 5473])).
% 2.14/2.30 tff(5476,plain,
% 2.14/2.30 (~r(s(s(s(elem!1))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5475, 106, 5467, 95, 5469])).
% 2.14/2.30 tff(5477,plain,
% 2.14/2.30 (b(s(s(s(elem!1))), s(z))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1807, 5476])).
% 2.14/2.30 tff(5478,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5479,plain,
% 2.14/2.30 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5480,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z))))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5479])).
% 2.14/2.30 tff(5481,plain,
% 2.14/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z)))))),
% 2.14/2.30 inference(transitivity,[status(thm)],[5480, 5478])).
% 2.14/2.30 tff(5482,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.14/2.30 inference(quant_inst,[status(thm)],[])).
% 2.14/2.30 tff(5483,plain,
% 2.14/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(s(z))))),
% 2.14/2.30 inference(modus_ponens,[status(thm)],[5482, 5481])).
% 2.14/2.30 tff(5484,plain,
% 2.14/2.30 ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5483, 171, 1596, 5392, 5423, 5419])).
% 2.14/2.30 tff(5485,plain,
% 2.14/2.30 (~b(s(z), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5484, 5477])).
% 2.14/2.30 tff(5486,plain,
% 2.14/2.30 (r(s(z), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[1444, 5485, 1651])).
% 2.14/2.30 tff(5487,plain,
% 2.14/2.30 (b(s(s(s(z))), elem!1)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[804, 4495, 797])).
% 2.14/2.30 tff(5488,plain,
% 2.14/2.30 (~b(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[5440, 171, 3137, 1596, 5487])).
% 2.14/2.30 tff(5489,plain,
% 2.14/2.30 (r(s(s(s(z))), z)),
% 2.14/2.30 inference(unit_resolution,[status(thm)],[953, 25, 194, 5488])).
% 2.14/2.30 tff(5490,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 2.14/2.30 tff(5491,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5492,plain,
% 2.14/2.30 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.14/2.30 inference(rewrite,[status(thm)],[])).
% 2.14/2.30 tff(5493,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 2.14/2.30 inference(monotonicity,[status(thm)],[5492])).
% 2.14/2.30 tff(5494,plain,
% 2.14/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5493, 5491])).
% 2.14/2.31 tff(5495,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5496,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5495, 5494])).
% 2.14/2.31 tff(5497,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5496, 106, 5490, 95, 747, 5489])).
% 2.14/2.31 tff(5498,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = elem!1) | (~r(s(z), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5499,plain,
% 2.14/2.31 (~r(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5498, 5486, 95, 3137, 1596, 5365, 5467, 730])).
% 2.14/2.31 tff(5500,plain,
% 2.14/2.31 (b(s(s(s(z))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1173, 5499])).
% 2.14/2.31 tff(5501,plain,
% 2.14/2.31 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), elem!1)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5091])).
% 2.14/2.31 tff(5502,plain,
% 2.14/2.31 (r(s(z), elem!1) <=> r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[5501])).
% 2.14/2.31 tff(5503,plain,
% 2.14/2.31 (r(s(z), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5486, 5502])).
% 2.14/2.31 tff(5504,plain,
% 2.14/2.31 (b(s(s(s(z))), s(s(s(s(s(z)))))) <=> b(s(s(s(z))), elem!1)),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5091])).
% 2.14/2.31 tff(5505,plain,
% 2.14/2.31 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(symmetry,[status(thm)],[5504])).
% 2.14/2.31 tff(5506,plain,
% 2.14/2.31 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5505])).
% 2.14/2.31 tff(5507,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5458, 5506])).
% 2.14/2.31 tff(5508,plain,
% 2.14/2.31 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[835, 5507, 5364])).
% 2.14/2.31 tff(5509,plain,
% 2.14/2.31 (~r(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3213, 5508, 5096, 5503, 5421])).
% 2.14/2.31 tff(5510,plain,
% 2.14/2.31 (b(s(z), s(s(s(z))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1996, 5509])).
% 2.14/2.31 tff(5511,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5512,plain,
% 2.14/2.31 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5513,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5512])).
% 2.14/2.31 tff(5514,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5513, 5511])).
% 2.14/2.31 tff(5515,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5516,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5515, 5514])).
% 2.14/2.31 tff(5517,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5516, 171, 259, 1188, 2705, 1976])).
% 2.14/2.31 tff(5518,plain,((~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(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5519,plain,
% 2.14/2.31 (~b(s(s(s(z))), s(s(z)))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5518, 5510, 259, 5500])).
% 2.14/2.31 tff(5520,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[2640, 25, 5519, 5465, 80])).
% 2.14/2.31 tff(5521,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(z))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (s(z) = elem!1) | (elem!1 = s(s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (s(s(s(s(s(z))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5522,plain,
% 2.14/2.31 (~r(s(s(z)), elem!1)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5521, 5356, 3137, 502, 730, 3829, 5359, 95, 1651, 3738, 1, 96, 259])).
% 2.14/2.31 tff(5523,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1416, 5522, 5357, 2116])).
% 2.14/2.31 tff(5524,plain,((z = elem!1) | (s(s(z)) = elem!1) | (~b(z, elem!1)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (s(z) = elem!1) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5525,plain,
% 2.14/2.31 (s(s(z)) = elem!1),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5524, 5354, 4901, 5343, 5342, 31, 5236, 5235, 94, 245])).
% 2.14/2.31 tff(5526,plain,
% 2.14/2.31 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5525])).
% 2.14/2.31 tff(5527,plain,
% 2.14/2.31 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.14/2.31 inference(symmetry,[status(thm)],[5526])).
% 2.14/2.31 tff(5528,plain,
% 2.14/2.31 (r(s(s(z)), s(z))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5342, 5527])).
% 2.14/2.31 tff(5529,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[235, 5528])).
% 2.14/2.31 tff(5530,plain,(b(z, 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(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5531,plain,
% 2.14/2.31 (b(z, s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5530, 83, 32, 5])).
% 2.14/2.31 tff(5532,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5533,plain,
% 2.14/2.31 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5534,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5533])).
% 2.14/2.31 tff(5535,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5534, 5532])).
% 2.14/2.31 tff(5536,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5537,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5536, 5535])).
% 2.14/2.31 tff(5538,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5537, 106, 95, 126, 502, 1288])).
% 2.14/2.31 tff(5539,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5540,plain,
% 2.14/2.31 (~r(z, s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5539, 502, 126, 95])).
% 2.14/2.31 tff(5541,plain,
% 2.14/2.31 (b(z, s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[498, 5540])).
% 2.14/2.31 tff(5542,plain,
% 2.14/2.31 (((~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(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5543,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5542])).
% 2.14/2.31 tff(5544,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5543, 4242])).
% 2.14/2.31 tff(5545,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5546,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 2.14/2.31 tff(5547,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5546, 171, 3686, 83, 1313, 2527])).
% 2.14/2.31 tff(5548,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5549,plain,
% 2.14/2.31 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5548, 2527, 83, 5541])).
% 2.14/2.31 tff(5550,plain,
% 2.14/2.31 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[3668, 5549])).
% 2.14/2.31 tff(5551,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[1325, 106, 95, 260, 502, 263])).
% 2.14/2.31 tff(5552,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5553,plain,
% 2.14/2.31 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5552, 5550, 502, 95])).
% 2.14/2.31 tff(5554,plain,
% 2.14/2.31 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[321, 5553, 255])).
% 2.14/2.31 tff(5555,plain,
% 2.14/2.31 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[534, 106, 5550, 126, 502])).
% 2.14/2.31 tff(5556,plain,
% 2.14/2.31 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[454, 5555, 254])).
% 2.14/2.31 tff(5557,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5558,plain,
% 2.14/2.31 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5559,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5558])).
% 2.14/2.31 tff(5560,plain,
% 2.14/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5559, 5557])).
% 2.14/2.31 tff(5561,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5562,plain,
% 2.14/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5561, 5560])).
% 2.14/2.31 tff(5563,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5562, 171, 3281, 5556, 5554, 2527])).
% 2.14/2.31 tff(5564,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5565,plain,
% 2.14/2.31 (~b(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5564, 502, 126, 3281, 95, 83])).
% 2.14/2.31 tff(5566,plain,
% 2.14/2.31 (r(z, s(s(s(s(z)))))),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[293, 5565])).
% 2.14/2.31 tff(5567,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.31 tff(5568,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5569,plain,
% 2.14/2.31 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(rewrite,[status(thm)],[])).
% 2.14/2.31 tff(5570,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.31 inference(monotonicity,[status(thm)],[5569])).
% 2.14/2.31 tff(5571,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.31 inference(transitivity,[status(thm)],[5570, 5568])).
% 2.14/2.31 tff(5572,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.14/2.31 inference(quant_inst,[status(thm)],[])).
% 2.14/2.31 tff(5573,plain,
% 2.14/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.31 inference(modus_ponens,[status(thm)],[5572, 5571])).
% 2.14/2.31 tff(5574,plain,
% 2.14/2.31 ($false),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5573, 106, 554, 637, 95, 5567])).
% 2.14/2.31 tff(5575,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.31 tff(5576,plain,
% 2.14/2.31 (~r(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[5575, 554, 95, 5566])).
% 2.14/2.31 tff(5577,plain,
% 2.14/2.31 (b(s(s(z)), z)),
% 2.14/2.31 inference(unit_resolution,[status(thm)],[157, 5576])).
% 2.14/2.31 tff(5578,plain,
% 2.14/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5579,plain,
% 2.14/2.32 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5580,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5579])).
% 2.14/2.32 tff(5581,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5580, 5578])).
% 2.14/2.32 tff(5582,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5583,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5582, 5581])).
% 2.14/2.32 tff(5584,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5583, 106, 95, 126, 5567, 127])).
% 2.14/2.32 tff(5585,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5586,plain,
% 2.14/2.32 (~r(s(s(s(s(s(z))))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5585, 5566, 126, 95])).
% 2.14/2.32 tff(5587,plain,
% 2.14/2.32 (b(s(s(s(s(s(z))))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[145, 5586])).
% 2.14/2.32 tff(5588,plain,
% 2.14/2.32 (~r(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5585, 127, 126, 95])).
% 2.14/2.32 tff(5589,plain,
% 2.14/2.32 (b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[293, 5588])).
% 2.14/2.32 tff(5590,plain,
% 2.14/2.32 (((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5591,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5590])).
% 2.14/2.32 tff(5592,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5591, 3430])).
% 2.14/2.32 tff(5593,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5594,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5593, 5592])).
% 2.14/2.32 tff(5595,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5594, 106, 95, 126, 127, 1288])).
% 2.14/2.32 tff(5596,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5597,plain,
% 2.14/2.32 (~r(z, s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5596, 127, 126, 95])).
% 2.14/2.32 tff(5598,plain,
% 2.14/2.32 (b(z, s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[498, 5597])).
% 2.14/2.32 tff(5599,plain,
% 2.14/2.32 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5548, 5598, 83, 5589])).
% 2.14/2.32 tff(5600,plain,
% 2.14/2.32 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[3668, 5599])).
% 2.14/2.32 tff(5601,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[302, 5600, 126, 127])).
% 2.14/2.32 tff(5602,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[321, 5601, 255])).
% 2.14/2.32 tff(5603,plain,
% 2.14/2.32 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[302, 260, 126, 127])).
% 2.14/2.32 tff(5604,plain,
% 2.14/2.32 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[321, 5603, 255])).
% 2.14/2.32 tff(5605,plain,
% 2.14/2.32 (~b(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[445, 5604, 376, 4])).
% 2.14/2.32 tff(5606,plain,
% 2.14/2.32 (r(s(s(z)), s(z))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[244, 5605])).
% 2.14/2.32 tff(5607,plain,
% 2.14/2.32 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[402, 171, 4, 376, 5604])).
% 2.14/2.32 tff(5608,plain,
% 2.14/2.32 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[427, 5607])).
% 2.14/2.32 tff(5609,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 2.14/2.32 tff(5610,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5611,plain,
% 2.14/2.32 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5612,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5611])).
% 2.14/2.32 tff(5613,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5612, 5610])).
% 2.14/2.32 tff(5614,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5615,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5614, 5613])).
% 2.14/2.32 tff(5616,plain,
% 2.14/2.32 (~r(s(s(z)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5615, 106, 96, 2, 126])).
% 2.14/2.32 tff(5617,plain,
% 2.14/2.32 (b(s(s(z)), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[157, 5616])).
% 2.14/2.32 tff(5618,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5619,plain,
% 2.14/2.32 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5620,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5619])).
% 2.14/2.32 tff(5621,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5620, 5618])).
% 2.14/2.32 tff(5622,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5623,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5622, 5621])).
% 2.14/2.32 tff(5624,plain,
% 2.14/2.32 (~r(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5623, 106, 96, 2, 126])).
% 2.14/2.32 tff(5625,plain,
% 2.14/2.32 (b(z, s(s(z)))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[124, 5624])).
% 2.14/2.32 tff(5626,plain,
% 2.14/2.32 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[177, 171, 5625, 5617, 159])).
% 2.14/2.32 tff(5627,plain,
% 2.14/2.32 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[203, 25, 5626, 198])).
% 2.14/2.32 tff(5628,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5629,plain,
% 2.14/2.32 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), 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(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5630,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(z), s(s(s(s(s(z)))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5629])).
% 2.14/2.32 tff(5631,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(z), s(s(s(s(s(z))))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5630, 5628])).
% 2.14/2.32 tff(5632,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5633,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5632, 5631])).
% 2.14/2.32 tff(5634,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5633, 106, 2, 5609, 126, 5627])).
% 2.14/2.32 tff(5635,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5636,plain,
% 2.14/2.32 (~b(s(s(s(s(s(z))))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5635, 96, 5609, 126, 2])).
% 2.14/2.32 tff(5637,plain,
% 2.14/2.32 (r(s(s(s(s(s(z))))), z)),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[145, 5636])).
% 2.14/2.32 tff(5638,plain,
% 2.14/2.32 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 2.14/2.32 inference(commutativity,[status(thm)],[])).
% 2.14/2.32 tff(5639,plain,
% 2.14/2.32 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 2.14/2.32 inference(symmetry,[status(thm)],[5638])).
% 2.14/2.32 tff(5640,plain,
% 2.14/2.32 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5639])).
% 2.14/2.32 tff(5641,plain,
% 2.14/2.32 (~(z = s(s(s(s(z)))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[52, 5640])).
% 2.14/2.32 tff(5642,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5643,plain,
% 2.14/2.32 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5644,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5643])).
% 2.14/2.32 tff(5645,plain,
% 2.14/2.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5644, 5642])).
% 2.14/2.32 tff(5646,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5647,plain,
% 2.14/2.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.32 inference(modus_ponens,[status(thm)],[5646, 5645])).
% 2.14/2.32 tff(5648,plain,
% 2.14/2.32 ($false),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5647, 106, 260, 5609, 5567, 127])).
% 2.14/2.32 tff(5649,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.32 tff(5650,plain,
% 2.14/2.32 (~r(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5649, 5637, 5609, 260])).
% 2.14/2.32 tff(5651,plain,
% 2.14/2.32 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[291, 25, 5650])).
% 2.14/2.32 tff(5652,plain,
% 2.14/2.32 (b(z, s(s(s(s(z)))))),
% 2.14/2.32 inference(unit_resolution,[status(thm)],[5651, 5641])).
% 2.14/2.32 tff(5653,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5654,plain,
% 2.14/2.32 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(rewrite,[status(thm)],[])).
% 2.14/2.32 tff(5655,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.32 inference(monotonicity,[status(thm)],[5654])).
% 2.14/2.32 tff(5656,plain,
% 2.14/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.32 inference(transitivity,[status(thm)],[5655, 5653])).
% 2.14/2.32 tff(5657,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 2.14/2.32 inference(quant_inst,[status(thm)],[])).
% 2.14/2.32 tff(5658,plain,
% 2.14/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5657, 5656])).
% 2.14/2.33 tff(5659,plain,
% 2.14/2.33 (~b(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5658, 171, 376, 357, 5652])).
% 2.14/2.33 tff(5660,plain,
% 2.14/2.33 (r(s(z), z)),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[30, 5659])).
% 2.14/2.33 tff(5661,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[133, 106, 96, 5660, 126, 5637])).
% 2.14/2.33 tff(5662,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5663,plain,
% 2.14/2.33 (~r(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5662, 5608, 376, 126, 5604, 260, 5606])).
% 2.14/2.33 tff(5664,plain,
% 2.14/2.33 (b(z, s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[93, 5663])).
% 2.14/2.33 tff(5665,plain,
% 2.14/2.33 (~b(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5562, 171, 5664, 376, 5604])).
% 2.14/2.33 tff(5666,plain,
% 2.14/2.33 (~r(z, s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5649, 5608, 127, 260])).
% 2.14/2.33 tff(5667,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[291, 25, 5666, 5665, 286])).
% 2.14/2.33 tff(5668,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5669,plain,
% 2.14/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5668, 260, 126, 127, 4])).
% 2.14/2.33 tff(5670,plain,
% 2.14/2.33 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 5669, 254])).
% 2.14/2.33 tff(5671,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), 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(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5672,plain,
% 2.14/2.33 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5673,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), 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(z), s(s(s(s(s(z)))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5672])).
% 2.14/2.33 tff(5674,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), 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(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5673, 5671])).
% 2.14/2.33 tff(5675,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5676,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5675, 5674])).
% 2.14/2.33 tff(5677,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5676, 106, 260, 126, 5670, 127])).
% 2.14/2.33 tff(5678,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5679,plain,
% 2.14/2.33 (~b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5678, 5600, 127, 126])).
% 2.14/2.33 tff(5680,plain,
% 2.14/2.33 (r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[479, 5679])).
% 2.14/2.33 tff(5681,plain,
% 2.14/2.33 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[534, 106, 5600, 126, 5680])).
% 2.14/2.33 tff(5682,plain,
% 2.14/2.33 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 5681, 254])).
% 2.14/2.33 tff(5683,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[232, 106, 2, 126, 396, 501])).
% 2.14/2.33 tff(5684,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5685,plain,
% 2.14/2.33 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5684, 396, 126, 2])).
% 2.14/2.33 tff(5686,plain,
% 2.14/2.33 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[205, 5685])).
% 2.14/2.33 tff(5687,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5688,plain,
% 2.14/2.33 (((~r(s(z), s(s(s(s(s(z))))))) | (~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))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5689,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5688])).
% 2.14/2.33 tff(5690,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5689, 5687])).
% 2.14/2.33 tff(5691,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5692,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5691, 5690])).
% 2.14/2.33 tff(5693,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5692, 106, 2, 126, 502, 396])).
% 2.14/2.33 tff(5694,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~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))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5695,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5694, 396, 126, 2])).
% 2.14/2.33 tff(5696,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[479, 5695])).
% 2.14/2.33 tff(5697,plain,
% 2.14/2.33 (~r(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[4802, 396, 2, 126])).
% 2.14/2.33 tff(5698,plain,
% 2.14/2.33 (b(s(z), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[550, 5697])).
% 2.14/2.33 tff(5699,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5700,plain,
% 2.14/2.33 (((~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(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(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5701,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5700])).
% 2.14/2.33 tff(5702,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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)))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5701, 5699])).
% 2.14/2.33 tff(5703,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5704,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(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))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 2.14/2.33 tff(5705,plain,
% 2.14/2.33 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5704, 171, 3686, 83, 160])).
% 2.14/2.33 tff(5706,plain,
% 2.14/2.33 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[374, 5705, 355])).
% 2.14/2.33 tff(5707,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5708,plain,
% 2.14/2.33 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5709,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5708])).
% 2.14/2.33 tff(5710,plain,
% 2.14/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5709, 5707])).
% 2.14/2.33 tff(5711,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5712,plain,
% 2.14/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5711, 5710])).
% 2.14/2.33 tff(5713,plain,
% 2.14/2.33 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5712, 171, 323, 3686, 83, 4, 160])).
% 2.14/2.33 tff(5714,plain,
% 2.14/2.33 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[321, 5713, 255])).
% 2.14/2.33 tff(5715,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5716,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.33 tff(5717,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.33 inference(modus_ponens,[status(thm)],[5716, 5715])).
% 2.14/2.33 tff(5718,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5717, 106, 2, 95, 5714, 5706])).
% 2.14/2.33 tff(5719,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(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(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5720,plain,
% 2.14/2.33 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5719, 5698, 95, 2, 83, 5696, 5686])).
% 2.14/2.33 tff(5721,plain,
% 2.14/2.33 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[3668, 5720])).
% 2.14/2.33 tff(5722,plain,
% 2.14/2.33 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[463, 5721, 126, 396])).
% 2.14/2.33 tff(5723,plain,
% 2.14/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5668, 5721, 126, 127, 5696])).
% 2.14/2.33 tff(5724,plain,
% 2.14/2.33 ($false),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[454, 5723, 5722, 254])).
% 2.14/2.33 tff(5725,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.33 tff(5726,plain,
% 2.14/2.33 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[5725, 127, 126, 95, 2, 83])).
% 2.14/2.33 tff(5727,plain,
% 2.14/2.33 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.33 inference(unit_resolution,[status(thm)],[225, 5726])).
% 2.14/2.33 tff(5728,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5729,plain,
% 2.14/2.33 (((~r(s(z), s(s(s(s(s(z))))))) | (~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)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(rewrite,[status(thm)],[])).
% 2.14/2.33 tff(5730,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.33 inference(monotonicity,[status(thm)],[5729])).
% 2.14/2.33 tff(5731,plain,
% 2.14/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(transitivity,[status(thm)],[5730, 5728])).
% 2.14/2.33 tff(5732,plain,
% 2.14/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.33 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5733,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 2.14/2.34 tff(5734,plain,
% 2.14/2.34 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5733, 106, 2, 126, 502])).
% 2.14/2.34 tff(5735,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5736,plain,
% 2.14/2.34 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5737,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5736])).
% 2.14/2.34 tff(5738,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5737, 5735])).
% 2.14/2.34 tff(5739,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5740,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5739, 5738])).
% 2.14/2.34 tff(5741,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5740, 106, 2, 126, 263])).
% 2.14/2.34 tff(5742,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[374, 5741, 369])).
% 2.14/2.34 tff(5743,plain,
% 2.14/2.34 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5694, 126, 2, 502])).
% 2.14/2.34 tff(5744,plain,
% 2.14/2.34 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[225, 5743])).
% 2.14/2.34 tff(5745,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5746,plain,
% 2.14/2.34 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5747,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5746])).
% 2.14/2.34 tff(5748,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5747, 5745])).
% 2.14/2.34 tff(5749,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5750,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5749, 5748])).
% 2.14/2.34 tff(5751,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5750, 106, 126, 502, 263])).
% 2.14/2.34 tff(5752,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[1156, 5751, 419])).
% 2.14/2.34 tff(5753,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5754,plain,
% 2.14/2.34 (((~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(z))))), 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(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(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5755,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5754])).
% 2.14/2.34 tff(5756,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5755, 5753])).
% 2.14/2.34 tff(5757,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5758,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5757, 5756])).
% 2.14/2.34 tff(5759,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5758, 171, 3686, 160, 207, 356])).
% 2.14/2.34 tff(5760,plain,((~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(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5761,plain,
% 2.14/2.34 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5760, 5752, 5744, 5742])).
% 2.14/2.34 tff(5762,plain,
% 2.14/2.34 ($false),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[203, 25, 5761, 5734, 198])).
% 2.14/2.34 tff(5763,plain,((~r(s(z), s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.34 tff(5764,plain,
% 2.14/2.34 ((~r(s(z), s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5763, 415])).
% 2.14/2.34 tff(5765,plain,
% 2.14/2.34 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5764, 502, 355, 126, 2])).
% 2.14/2.34 tff(5766,plain,
% 2.14/2.34 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[321, 5765, 255])).
% 2.14/2.34 tff(5767,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5768,plain,
% 2.14/2.34 (((~r(s(z), s(s(z)))) | (~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)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5769,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5768])).
% 2.14/2.34 tff(5770,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5769, 5767])).
% 2.14/2.34 tff(5771,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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))))))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5772,plain,
% 2.14/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5771, 5770])).
% 2.14/2.34 tff(5773,plain,
% 2.14/2.34 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5772, 106, 554, 2, 502])).
% 2.14/2.34 tff(5774,plain,
% 2.14/2.34 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[205, 5773])).
% 2.14/2.34 tff(5775,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5776,plain,
% 2.14/2.34 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5777,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5776])).
% 2.14/2.34 tff(5778,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5777, 5775])).
% 2.14/2.34 tff(5779,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5780,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5779, 5778])).
% 2.14/2.34 tff(5781,plain,
% 2.14/2.34 (~b(s(s(s(s(z)))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5780, 171, 3686, 160, 207, 1313])).
% 2.14/2.34 tff(5782,plain,
% 2.14/2.34 (r(s(s(s(s(z)))), z)),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[272, 25, 52, 5781])).
% 2.14/2.34 tff(5783,plain,
% 2.14/2.34 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5760, 3686, 207, 160])).
% 2.14/2.34 tff(5784,plain,
% 2.14/2.34 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[374, 5783, 369])).
% 2.14/2.34 tff(5785,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5786,plain,
% 2.14/2.34 (((~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(z))))), 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(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(rewrite,[status(thm)],[])).
% 2.14/2.34 tff(5787,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.14/2.34 inference(monotonicity,[status(thm)],[5786])).
% 2.14/2.34 tff(5788,plain,
% 2.14/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.34 inference(transitivity,[status(thm)],[5787, 5785])).
% 2.14/2.34 tff(5789,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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)))))),
% 2.14/2.34 inference(quant_inst,[status(thm)],[])).
% 2.14/2.34 tff(5790,plain,
% 2.14/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.34 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 2.14/2.34 tff(5791,plain,
% 2.14/2.34 (~b(z, s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[5790, 171, 160, 207, 1313])).
% 2.14/2.34 tff(5792,plain,
% 2.14/2.34 (r(z, s(s(z)))),
% 2.14/2.34 inference(unit_resolution,[status(thm)],[124, 5791])).
% 2.14/2.34 tff(5793,plain,
% 2.14/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5794,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5795,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5794, 5793])).
% 2.14/2.35 tff(5796,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5795, 106, 2, 5792, 5784, 5782])).
% 2.14/2.35 tff(5797,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5798,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5797, 5774, 2, 207, 5541, 355])).
% 2.14/2.35 tff(5799,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[3668, 5798])).
% 2.14/2.35 tff(5800,plain,
% 2.14/2.35 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[534, 106, 5799, 126, 502])).
% 2.14/2.35 tff(5801,plain,
% 2.14/2.35 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[454, 5800, 254])).
% 2.14/2.35 tff(5802,plain,
% 2.14/2.35 (~b(z, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5562, 171, 3281, 5801, 5766])).
% 2.14/2.35 tff(5803,plain,
% 2.14/2.35 (r(z, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[293, 5802])).
% 2.14/2.35 tff(5804,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5805,plain,
% 2.14/2.35 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, 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(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5806,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5805])).
% 2.14/2.35 tff(5807,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5806, 5804])).
% 2.14/2.35 tff(5808,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(s(s(z)), z)))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5809,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5808, 5807])).
% 2.14/2.35 tff(5810,plain,
% 2.14/2.35 (~b(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5809, 171, 3281, 83, 5774, 5766, 5541])).
% 2.14/2.35 tff(5811,plain,
% 2.14/2.35 (r(s(s(z)), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[157, 5810])).
% 2.14/2.35 tff(5812,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5575, 5811, 5803, 95, 554])).
% 2.14/2.35 tff(5813,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5814,plain,
% 2.14/2.35 (~r(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5813, 5680, 95, 3281, 83, 126, 2, 5727])).
% 2.14/2.35 tff(5815,plain,
% 2.14/2.35 (b(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[550, 5814])).
% 2.14/2.35 tff(5816,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5817,plain,
% 2.14/2.35 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5818,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5817])).
% 2.14/2.35 tff(5819,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5818, 5816])).
% 2.14/2.35 tff(5820,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5821,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5820, 5819])).
% 2.14/2.35 tff(5822,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5821, 171, 5815, 3281, 5682, 5602, 5589])).
% 2.14/2.35 tff(5823,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5824,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5823, 2, 126, 95, 83, 3281])).
% 2.14/2.35 tff(5825,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[145, 5824])).
% 2.14/2.35 tff(5826,plain,
% 2.14/2.35 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5694, 502, 126, 2])).
% 2.14/2.35 tff(5827,plain,
% 2.14/2.35 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[225, 5826])).
% 2.14/2.35 tff(5828,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5829,plain,
% 2.14/2.35 (((~r(s(z), z)) | (~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)))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5830,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5829])).
% 2.14/2.35 tff(5831,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5830, 5828])).
% 2.14/2.35 tff(5832,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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))))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5833,plain,
% 2.14/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 2.14/2.35 tff(5834,plain,
% 2.14/2.35 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5833, 106, 2, 95, 502])).
% 2.14/2.35 tff(5835,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[205, 5834])).
% 2.14/2.35 tff(5836,plain,
% 2.14/2.35 (~r(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5813, 5827, 95, 3281, 83, 126, 2, 502])).
% 2.14/2.35 tff(5837,plain,
% 2.14/2.35 (b(s(z), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[550, 5836])).
% 2.14/2.35 tff(5838,plain,
% 2.14/2.35 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(z)))),
% 2.14/2.35 inference(commutativity,[status(thm)],[])).
% 2.14/2.35 tff(5839,plain,
% 2.14/2.35 ((s(s(s(s(s(z))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.14/2.35 inference(symmetry,[status(thm)],[5838])).
% 2.14/2.35 tff(5840,plain,
% 2.14/2.35 ((~(s(s(s(s(s(z))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5839])).
% 2.14/2.35 tff(5841,plain,
% 2.14/2.35 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[196, 5840])).
% 2.14/2.35 tff(5842,plain,
% 2.14/2.35 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[203, 25, 5834])).
% 2.14/2.35 tff(5843,plain,
% 2.14/2.35 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5842, 5841])).
% 2.14/2.35 tff(5844,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5845,plain,
% 2.14/2.35 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5846,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5845])).
% 2.14/2.35 tff(5847,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5846, 5844])).
% 2.14/2.35 tff(5848,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5849,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5848, 5847])).
% 2.14/2.35 tff(5850,plain,
% 2.14/2.35 ($false),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5849, 171, 323, 5843, 4677, 357, 356])).
% 2.14/2.35 tff(5851,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.35 tff(5852,plain,
% 2.14/2.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5851, 5766, 95, 2, 323, 502])).
% 2.14/2.35 tff(5853,plain,
% 2.14/2.35 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[374, 5852, 355])).
% 2.14/2.35 tff(5854,plain,
% 2.14/2.35 (~b(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[215, 5827, 159, 1])).
% 2.14/2.35 tff(5855,plain,
% 2.14/2.35 (r(z, s(s(z)))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[124, 5854])).
% 2.14/2.35 tff(5856,plain,
% 2.14/2.35 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5795, 106, 2, 600])).
% 2.14/2.35 tff(5857,plain,
% 2.14/2.35 (~r(s(s(s(s(z)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5856, 569])).
% 2.14/2.35 tff(5858,plain,
% 2.14/2.35 (b(s(s(s(s(z)))), z)),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[272, 25, 52, 5857])).
% 2.14/2.35 tff(5859,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5860,plain,
% 2.14/2.35 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(rewrite,[status(thm)],[])).
% 2.14/2.35 tff(5861,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.35 inference(monotonicity,[status(thm)],[5860])).
% 2.14/2.35 tff(5862,plain,
% 2.14/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(transitivity,[status(thm)],[5861, 5859])).
% 2.14/2.35 tff(5863,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.35 inference(quant_inst,[status(thm)],[])).
% 2.14/2.35 tff(5864,plain,
% 2.14/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.35 inference(modus_ponens,[status(thm)],[5863, 5862])).
% 2.14/2.35 tff(5865,plain,
% 2.14/2.35 (~b(z, s(s(s(s(z)))))),
% 2.14/2.35 inference(unit_resolution,[status(thm)],[5864, 171, 323, 3281, 1, 357, 5858])).
% 2.14/2.35 tff(5866,plain,
% 2.14/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5867,plain,
% 2.14/2.36 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5868,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5867])).
% 2.14/2.36 tff(5869,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5868, 5866])).
% 2.14/2.36 tff(5870,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5871,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5870, 5869])).
% 2.14/2.36 tff(5872,plain,
% 2.14/2.36 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5871, 106, 2, 600])).
% 2.14/2.36 tff(5873,plain,
% 2.14/2.36 (~r(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5872, 569])).
% 2.14/2.36 tff(5874,plain,
% 2.14/2.36 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[291, 25, 5873])).
% 2.14/2.36 tff(5875,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5874, 5865, 5641])).
% 2.14/2.36 tff(5876,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5877,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5876, 5855, 5853, 2, 323, 3281, 1, 5766])).
% 2.14/2.36 tff(5878,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5879,plain,
% 2.14/2.36 (~b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5878, 5837, 5825, 3281, 2, 502, 95, 126])).
% 2.14/2.36 tff(5880,plain,
% 2.14/2.36 (r(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[157, 5879])).
% 2.14/2.36 tff(5881,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5851, 5837, 95, 2, 502, 5766])).
% 2.14/2.36 tff(5882,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[374, 5881, 355])).
% 2.14/2.36 tff(5883,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5797, 5835, 2, 5827, 5541, 355])).
% 2.14/2.36 tff(5884,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3668, 5883])).
% 2.14/2.36 tff(5885,plain,
% 2.14/2.36 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[534, 106, 5884, 126, 502])).
% 2.14/2.36 tff(5886,plain,
% 2.14/2.36 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[454, 5885, 254])).
% 2.14/2.36 tff(5887,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5888,plain,
% 2.14/2.36 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5889,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5888])).
% 2.14/2.36 tff(5890,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5889, 5887])).
% 2.14/2.36 tff(5891,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5892,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5891, 5890])).
% 2.14/2.36 tff(5893,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5892, 171, 3281, 5886, 5766])).
% 2.14/2.36 tff(5894,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[274, 5893])).
% 2.14/2.36 tff(5895,plain,
% 2.14/2.36 (~r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[3707, 5894, 5882, 5880])).
% 2.14/2.36 tff(5896,plain,
% 2.14/2.36 (b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[124, 5895])).
% 2.14/2.36 tff(5897,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5898,plain,
% 2.14/2.36 (((~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(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(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5899,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(s(s(s(z))))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5898])).
% 2.14/2.36 tff(5900,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(s(s(s(z)))))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5899, 5897])).
% 2.14/2.36 tff(5901,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5902,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5901, 5900])).
% 2.14/2.36 tff(5903,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5902, 171, 5896, 83, 5835, 5827, 5541])).
% 2.14/2.36 tff(5904,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5905,plain,
% 2.14/2.36 (~r(s(s(s(s(s(z))))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5904, 2, 3281, 126, 83, 95])).
% 2.14/2.36 tff(5906,plain,
% 2.14/2.36 (b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[479, 5905])).
% 2.14/2.36 tff(5907,plain,
% 2.14/2.36 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[4802, 554, 2, 126])).
% 2.14/2.36 tff(5908,plain,
% 2.14/2.36 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[225, 5907])).
% 2.14/2.36 tff(5909,plain,
% 2.14/2.36 (~b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[215, 5908, 159, 1])).
% 2.14/2.36 tff(5910,plain,
% 2.14/2.36 (r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[124, 5909])).
% 2.14/2.36 tff(5911,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5912,plain,
% 2.14/2.36 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5913,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5912])).
% 2.14/2.36 tff(5914,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5913, 5911])).
% 2.14/2.36 tff(5915,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5916,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5915, 5914])).
% 2.14/2.36 tff(5917,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5916, 106, 554, 2, 95, 5910])).
% 2.14/2.36 tff(5918,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5919,plain,
% 2.14/2.36 (~b(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5918, 554, 95, 5825, 2, 126])).
% 2.14/2.36 tff(5920,plain,
% 2.14/2.36 (r(s(s(z)), z)),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[157, 5919])).
% 2.14/2.36 tff(5921,plain,
% 2.14/2.36 (~r(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5575, 5920, 95, 554])).
% 2.14/2.36 tff(5922,plain,
% 2.14/2.36 (b(z, s(s(s(s(z)))))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[293, 5921])).
% 2.14/2.36 tff(5923,plain,
% 2.14/2.36 (~r(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[2952, 5920, 554, 95])).
% 2.14/2.36 tff(5924,plain,
% 2.14/2.36 (b(z, s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[124, 5923])).
% 2.14/2.36 tff(5925,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5926,plain,
% 2.14/2.36 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5927,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5926])).
% 2.14/2.36 tff(5928,plain,
% 2.14/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5927, 5925])).
% 2.14/2.36 tff(5929,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5930,plain,
% 2.14/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5929, 5928])).
% 2.14/2.36 tff(5931,plain,
% 2.14/2.36 ($false),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5930, 171, 3281, 161, 4, 376, 159, 356])).
% 2.14/2.36 tff(5932,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.36 tff(5933,plain,
% 2.14/2.36 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5932, 376, 161, 4, 3281, 159])).
% 2.14/2.36 tff(5934,plain,
% 2.14/2.36 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[374, 5933, 355])).
% 2.14/2.36 tff(5935,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5936,plain,
% 2.14/2.36 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.36 inference(rewrite,[status(thm)],[])).
% 2.14/2.36 tff(5937,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.36 inference(monotonicity,[status(thm)],[5936])).
% 2.14/2.36 tff(5938,plain,
% 2.14/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.36 inference(transitivity,[status(thm)],[5937, 5935])).
% 2.14/2.36 tff(5939,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.14/2.36 inference(quant_inst,[status(thm)],[])).
% 2.14/2.36 tff(5940,plain,
% 2.14/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.36 inference(modus_ponens,[status(thm)],[5939, 5938])).
% 2.14/2.36 tff(5941,plain,
% 2.14/2.36 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[5940, 106, 554, 2, 5934])).
% 2.14/2.36 tff(5942,plain,
% 2.14/2.36 (b(s(s(s(s(z)))), s(z))),
% 2.14/2.36 inference(unit_resolution,[status(thm)],[321, 5941, 255])).
% 2.14/2.37 tff(5943,plain,
% 2.14/2.37 (((~b(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(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(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5944,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5943])).
% 2.14/2.37 tff(5945,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5944, 397])).
% 2.14/2.37 tff(5946,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5947,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5946, 5945])).
% 2.14/2.37 tff(5948,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5947, 171, 83, 4, 376, 5942])).
% 2.14/2.37 tff(5949,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5950,plain,
% 2.14/2.37 (~b(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5949, 554, 5906, 83, 2, 5924, 3281, 5825])).
% 2.14/2.37 tff(5951,plain,
% 2.14/2.37 (r(s(z), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[454, 5950, 254])).
% 2.14/2.37 tff(5952,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5953,plain,
% 2.14/2.37 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5954,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5953])).
% 2.14/2.37 tff(5955,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5954, 5952])).
% 2.14/2.37 tff(5956,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5957,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5956, 5955])).
% 2.14/2.37 tff(5958,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5957, 106, 554, 637, 95, 1288])).
% 2.14/2.37 tff(5959,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5960,plain,
% 2.14/2.37 (~r(z, s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5959, 5920, 554, 95])).
% 2.14/2.37 tff(5961,plain,
% 2.14/2.37 (b(z, s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[498, 5960])).
% 2.14/2.37 tff(5962,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5548, 5922, 83, 5961])).
% 2.14/2.37 tff(5963,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[3668, 5962])).
% 2.14/2.37 tff(5964,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5965,plain,
% 2.14/2.37 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5966,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5965])).
% 2.14/2.37 tff(5967,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5966, 5964])).
% 2.14/2.37 tff(5968,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5969,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5968, 5967])).
% 2.14/2.37 tff(5970,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5969, 106, 2, 260, 3, 500])).
% 2.14/2.37 tff(5971,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5972,plain,
% 2.14/2.37 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5971, 5963, 2, 5951])).
% 2.14/2.37 tff(5973,plain,
% 2.14/2.37 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[351, 5972])).
% 2.14/2.37 tff(5974,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5975,plain,
% 2.14/2.37 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, 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(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5976,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5975])).
% 2.14/2.37 tff(5977,plain,
% 2.14/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5976, 5974])).
% 2.14/2.37 tff(5978,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5979,plain,
% 2.14/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5978, 5977])).
% 2.14/2.37 tff(5980,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5979, 171, 161, 356, 2527, 2352])).
% 2.14/2.37 tff(5981,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(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5982,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5981, 5973, 5924, 5922])).
% 2.14/2.37 tff(5983,plain,
% 2.14/2.37 (r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[374, 5982, 355])).
% 2.14/2.37 tff(5984,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5985,plain,
% 2.14/2.37 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5986,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5985])).
% 2.14/2.37 tff(5987,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5986, 5984])).
% 2.14/2.37 tff(5988,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5989,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5988, 5987])).
% 2.14/2.37 tff(5990,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5989, 106, 554, 2, 5951, 5983])).
% 2.14/2.37 tff(5991,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(5992,plain,
% 2.14/2.37 (~r(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5991, 2, 83, 3281, 95, 126])).
% 2.14/2.37 tff(5993,plain,
% 2.14/2.37 (b(s(z), s(s(z)))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[550, 5992])).
% 2.14/2.37 tff(5994,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5995,plain,
% 2.14/2.37 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(5996,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[5995])).
% 2.14/2.37 tff(5997,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[5996, 5994])).
% 2.14/2.37 tff(5998,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(5999,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[5998, 5997])).
% 2.14/2.37 tff(6000,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5999, 106, 2, 637, 95, 600])).
% 2.14/2.37 tff(6001,plain,((~r(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(6002,plain,
% 2.14/2.37 (~r(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6001, 600, 95, 2])).
% 2.14/2.37 tff(6003,plain,
% 2.14/2.37 (b(s(s(z)), z)),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[157, 6002])).
% 2.14/2.37 tff(6004,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(6005,plain,
% 2.14/2.37 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(rewrite,[status(thm)],[])).
% 2.14/2.37 tff(6006,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.14/2.37 inference(monotonicity,[status(thm)],[6005])).
% 2.14/2.37 tff(6007,plain,
% 2.14/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(transitivity,[status(thm)],[6006, 6004])).
% 2.14/2.37 tff(6008,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.14/2.37 inference(quant_inst,[status(thm)],[])).
% 2.14/2.37 tff(6009,plain,
% 2.14/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.14/2.37 inference(modus_ponens,[status(thm)],[6008, 6007])).
% 2.14/2.37 tff(6010,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6009, 106, 2, 3, 263, 569])).
% 2.14/2.37 tff(6011,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.37 tff(6012,plain,
% 2.14/2.37 (~r(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[6011, 569, 2, 3])).
% 2.14/2.37 tff(6013,plain,
% 2.14/2.37 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[5876, 569, 2, 600, 3281, 323, 1])).
% 2.14/2.37 tff(6014,plain,
% 2.14/2.37 ($false),
% 2.14/2.37 inference(unit_resolution,[status(thm)],[321, 6013, 6012, 255])).
% 2.14/2.38 tff(6015,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(6016,plain,
% 2.14/2.38 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6015, 600, 2, 3281, 5993, 6003, 3])).
% 2.14/2.38 tff(6017,plain,
% 2.14/2.38 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[374, 6016, 355])).
% 2.14/2.38 tff(6018,plain,
% 2.14/2.38 ((z = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = z)),
% 2.14/2.38 inference(commutativity,[status(thm)],[])).
% 2.14/2.38 tff(6019,plain,
% 2.14/2.38 ((s(s(s(s(s(z))))) = z) <=> (z = s(s(s(s(s(z))))))),
% 2.14/2.38 inference(symmetry,[status(thm)],[6018])).
% 2.14/2.38 tff(6020,plain,
% 2.14/2.38 ((~(s(s(s(s(s(z))))) = z)) <=> (~(z = s(s(s(s(s(z)))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6019])).
% 2.14/2.38 tff(6021,plain,
% 2.14/2.38 (~(z = s(s(s(s(s(z))))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[140, 6020])).
% 2.14/2.38 tff(6022,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6023,plain,
% 2.14/2.38 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6024,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6023])).
% 2.14/2.38 tff(6025,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[6024, 6022])).
% 2.14/2.38 tff(6026,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(6027,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[6026, 6025])).
% 2.14/2.38 tff(6028,plain,
% 2.14/2.38 (~r(s(s(s(s(s(z))))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6027, 106, 2, 600, 396])).
% 2.14/2.38 tff(6029,plain,
% 2.14/2.38 (b(s(s(s(s(s(z))))), z)),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[143, 25, 140, 6028])).
% 2.14/2.38 tff(6030,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6031,plain,
% 2.14/2.38 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6032,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6031])).
% 2.14/2.38 tff(6033,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.38 inference(transitivity,[status(thm)],[6032, 6030])).
% 2.14/2.38 tff(6034,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(6035,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[6034, 6033])).
% 2.14/2.38 tff(6036,plain,
% 2.14/2.38 (~b(z, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6035, 171, 323, 3281, 1, 4, 6029])).
% 2.14/2.38 tff(6037,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6038,plain,
% 2.14/2.38 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6039,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6038])).
% 2.14/2.38 tff(6040,plain,
% 2.14/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[6039, 6037])).
% 2.14/2.38 tff(6041,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(6042,plain,
% 2.14/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[6041, 6040])).
% 2.14/2.38 tff(6043,plain,
% 2.14/2.38 (~r(z, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6042, 106, 2, 600, 396])).
% 2.14/2.38 tff(6044,plain,
% 2.14/2.38 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[496, 25, 6043])).
% 2.14/2.38 tff(6045,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6044, 6036, 6021])).
% 2.14/2.38 tff(6046,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(6047,plain,
% 2.14/2.38 (~b(s(s(s(s(s(z))))), s(z))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6046, 396, 3281, 1, 323, 2, 600])).
% 2.14/2.38 tff(6048,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[479, 5695, 6047])).
% 2.14/2.38 tff(6049,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(6050,plain,
% 2.14/2.38 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6049, 6003, 2, 3281, 126, 600, 5993])).
% 2.14/2.38 tff(6051,plain,
% 2.14/2.38 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[225, 6050])).
% 2.14/2.38 tff(6052,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6053,plain,
% 2.14/2.38 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6054,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6053])).
% 2.14/2.38 tff(6055,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.14/2.38 inference(transitivity,[status(thm)],[6054, 6052])).
% 2.14/2.38 tff(6056,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.14/2.38 inference(quant_inst,[status(thm)],[])).
% 2.14/2.38 tff(6057,plain,
% 2.14/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.14/2.38 inference(modus_ponens,[status(thm)],[6056, 6055])).
% 2.14/2.38 tff(6058,plain,
% 2.14/2.38 ($false),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6057, 171, 3281, 1, 3686, 4, 207, 356])).
% 2.14/2.38 tff(6059,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.38 tff(6060,plain,
% 2.14/2.38 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[6059, 6003, 3281, 5906, 6051, 6017])).
% 2.14/2.38 tff(6061,plain,
% 2.14/2.38 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[3668, 6060])).
% 2.14/2.38 tff(6062,plain,
% 2.14/2.38 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[5971, 6061, 2, 3])).
% 2.14/2.38 tff(6063,plain,
% 2.14/2.38 (b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.38 inference(unit_resolution,[status(thm)],[351, 6062])).
% 2.14/2.38 tff(6064,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6065,plain,
% 2.14/2.38 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(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(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.38 inference(rewrite,[status(thm)],[])).
% 2.14/2.38 tff(6066,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.14/2.38 inference(monotonicity,[status(thm)],[6065])).
% 2.14/2.38 tff(6067,plain,
% 2.14/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6066, 6064])).
% 2.14/2.39 tff(6068,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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)))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6069,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6068, 6067])).
% 2.14/2.39 tff(6070,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6069, 171, 6003, 83, 6051, 6017, 6063])).
% 2.14/2.39 tff(6071,plain,((~r(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6072,plain,
% 2.14/2.39 (~r(z, s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6071, 3, 2, 83, 3281, 126, 95])).
% 2.14/2.39 tff(6073,plain,
% 2.14/2.39 (b(z, s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[124, 6072])).
% 2.14/2.39 tff(6074,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6075,plain,
% 2.14/2.39 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6076,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6075])).
% 2.14/2.39 tff(6077,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6076, 6074])).
% 2.14/2.39 tff(6078,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6079,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6078, 6077])).
% 2.14/2.39 tff(6080,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6079, 106, 95, 260, 5567, 3])).
% 2.14/2.39 tff(6081,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6082,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6081, 5567, 95, 3])).
% 2.14/2.39 tff(6083,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3668, 6082])).
% 2.14/2.39 tff(6084,plain,
% 2.14/2.39 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5719, 6083, 95, 2, 83, 4, 323])).
% 2.14/2.39 tff(6085,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[205, 6084])).
% 2.14/2.39 tff(6086,plain,
% 2.14/2.39 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5684, 6085, 126, 2])).
% 2.14/2.39 tff(6087,plain,
% 2.14/2.39 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[225, 6086])).
% 2.14/2.39 tff(6088,plain,
% 2.14/2.39 (~b(s(s(z)), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[215, 6087, 159, 161])).
% 2.14/2.39 tff(6089,plain,
% 2.14/2.39 (r(s(s(z)), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[157, 6088])).
% 2.14/2.39 tff(6090,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6091,plain,
% 2.14/2.39 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6092,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6091])).
% 2.14/2.39 tff(6093,plain,
% 2.14/2.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6092, 6090])).
% 2.14/2.39 tff(6094,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6095,plain,
% 2.14/2.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6094, 6093])).
% 2.14/2.39 tff(6096,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6095, 106, 2, 6089, 95, 5567])).
% 2.14/2.39 tff(6097,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6098,plain,
% 2.14/2.39 (~r(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6097, 6073, 95, 5825, 2, 126, 83, 5906, 5993, 3])).
% 2.14/2.39 tff(6099,plain,
% 2.14/2.39 (b(z, s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[293, 6098])).
% 2.14/2.39 tff(6100,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5225, 171, 323, 161, 83, 159, 357, 2527])).
% 2.14/2.39 tff(6101,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(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(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6102,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6101, 6099, 6073, 83, 5825, 5993])).
% 2.14/2.39 tff(6103,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[321, 6102, 255])).
% 2.14/2.39 tff(6104,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6011, 6103, 2, 3])).
% 2.14/2.39 tff(6105,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[374, 6104, 355])).
% 2.14/2.39 tff(6106,plain,
% 2.14/2.39 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5981, 6105, 6073, 6099])).
% 2.14/2.39 tff(6107,plain,
% 2.14/2.39 (r(s(s(z)), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[351, 6106])).
% 2.14/2.39 tff(6108,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5971, 6107, 2, 3])).
% 2.14/2.39 tff(6109,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[3668, 6108])).
% 2.14/2.39 tff(6110,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6111,plain,
% 2.14/2.39 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6112,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6111])).
% 2.14/2.39 tff(6113,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6112, 6110])).
% 2.14/2.39 tff(6114,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, 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(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6115,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6114, 6113])).
% 2.14/2.39 tff(6116,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6115, 171, 3281, 6109, 83, 5906, 5825, 6099])).
% 2.14/2.39 tff(6117,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6118,plain,
% 2.14/2.39 (~r(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6117, 2, 83, 3281, 95, 126])).
% 2.14/2.39 tff(6119,plain,
% 2.14/2.39 (b(s(z), s(s(s(s(z)))))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[454, 6118, 254])).
% 2.14/2.39 tff(6120,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5876, 569, 2, 600, 3281, 323, 6003])).
% 2.14/2.39 tff(6121,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[321, 6120, 255])).
% 2.14/2.39 tff(6122,plain,
% 2.14/2.39 ($false),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[5717, 106, 2, 95, 6121, 569])).
% 2.14/2.39 tff(6123,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.39 tff(6124,plain,
% 2.14/2.39 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6123, 600, 95, 2, 3281, 323])).
% 2.14/2.39 tff(6125,plain,
% 2.14/2.39 (b(s(s(s(s(z)))), s(s(z)))),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[374, 6124, 355])).
% 2.14/2.39 tff(6126,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6127,plain,
% 2.14/2.39 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6128,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6127])).
% 2.14/2.39 tff(6129,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6128, 6126])).
% 2.14/2.39 tff(6130,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6131,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.14/2.39 inference(modus_ponens,[status(thm)],[6130, 6129])).
% 2.14/2.39 tff(6132,plain,
% 2.14/2.39 (~b(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[6131, 171, 323, 3281, 83, 159, 6125])).
% 2.14/2.39 tff(6133,plain,
% 2.14/2.39 (r(s(s(s(s(z)))), z)),
% 2.14/2.39 inference(unit_resolution,[status(thm)],[274, 6132])).
% 2.14/2.39 tff(6134,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6135,plain,
% 2.14/2.39 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(rewrite,[status(thm)],[])).
% 2.14/2.39 tff(6136,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.14/2.39 inference(monotonicity,[status(thm)],[6135])).
% 2.14/2.39 tff(6137,plain,
% 2.14/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(transitivity,[status(thm)],[6136, 6134])).
% 2.14/2.39 tff(6138,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.14/2.39 inference(quant_inst,[status(thm)],[])).
% 2.14/2.39 tff(6139,plain,
% 2.14/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.14/2.40 inference(modus_ponens,[status(thm)],[6138, 6137])).
% 2.14/2.40 tff(6140,plain,
% 2.14/2.40 (~b(s(s(s(s(z)))), s(z))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6139, 171, 83, 4, 376, 6125])).
% 2.14/2.40 tff(6141,plain,
% 2.14/2.40 (r(s(s(s(s(z)))), s(z))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[321, 6140, 255])).
% 2.14/2.40 tff(6142,plain,
% 2.14/2.40 ($false),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[2126, 6141, 6133, 95, 600])).
% 2.14/2.40 tff(6143,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.14/2.40 tff(6144,plain,
% 2.14/2.40 (~r(z, s(s(z)))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[6143, 5906, 83, 95, 6119, 5993, 3281, 5825, 2])).
% 2.14/2.40 tff(6145,plain,
% 2.14/2.40 (b(z, s(s(z)))),
% 2.14/2.40 inference(unit_resolution,[status(thm)],[124, 6144])).
% 2.14/2.40 tff(6146,plain,
% 2.14/2.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5932, 6145, 6119, 5906, 3281, 5825])).
% 2.24/2.40 tff(6147,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[374, 6146, 355])).
% 2.24/2.40 tff(6148,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5717, 106, 2, 95, 263, 569])).
% 2.24/2.40 tff(6149,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6150,plain,
% 2.24/2.40 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6149, 2, 95, 6147])).
% 2.24/2.40 tff(6151,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[321, 6150, 255])).
% 2.24/2.40 tff(6152,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6153,plain,
% 2.24/2.40 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6154,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6153])).
% 2.24/2.40 tff(6155,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6154, 6152])).
% 2.24/2.40 tff(6156,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(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(z))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6157,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6156, 6155])).
% 2.24/2.40 tff(6158,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6157, 171, 5993, 83, 5906, 6119, 6151])).
% 2.24/2.40 tff(6159,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6160,plain,
% 2.24/2.40 (~r(s(s(z)), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6159, 83, 95, 3281, 126])).
% 2.24/2.40 tff(6161,plain,
% 2.24/2.40 (b(s(s(z)), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[244, 6160])).
% 2.24/2.40 tff(6162,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6163,plain,
% 2.24/2.40 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6164,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6163])).
% 2.24/2.40 tff(6165,plain,
% 2.24/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6164, 6162])).
% 2.24/2.40 tff(6166,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6167,plain,
% 2.24/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6166, 6165])).
% 2.24/2.40 tff(6168,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6167, 106, 554, 126, 502, 501])).
% 2.24/2.40 tff(6169,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6170,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6169, 554, 126, 502])).
% 2.24/2.40 tff(6171,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[205, 6170])).
% 2.24/2.40 tff(6172,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[4606, 6171, 83, 95, 5587, 554, 5577])).
% 2.24/2.40 tff(6173,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3668, 6172])).
% 2.24/2.40 tff(6174,plain,
% 2.24/2.40 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[5552, 6173, 502, 95])).
% 2.24/2.40 tff(6175,plain,
% 2.24/2.40 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[321, 6174, 255])).
% 2.24/2.40 tff(6176,plain,
% 2.24/2.40 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6081, 6173, 95, 5566])).
% 2.24/2.40 tff(6177,plain,
% 2.24/2.40 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[454, 6176, 254])).
% 2.24/2.40 tff(6178,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6179,plain,
% 2.24/2.40 (((~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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6180,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6179])).
% 2.24/2.40 tff(6181,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6180, 6178])).
% 2.24/2.40 tff(6182,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6183,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6182, 6181])).
% 2.24/2.40 tff(6184,plain,
% 2.24/2.40 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6183, 171, 259, 3686, 376, 357])).
% 2.24/2.40 tff(6185,plain,
% 2.24/2.40 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[349, 25, 346, 6184])).
% 2.24/2.40 tff(6186,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6187,plain,
% 2.24/2.40 (((~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(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6188,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6187])).
% 2.24/2.40 tff(6189,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6188, 6186])).
% 2.24/2.40 tff(6190,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6191,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6190, 6189])).
% 2.24/2.40 tff(6192,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6191, 171, 3281, 3686, 376, 357, 2527])).
% 2.24/2.40 tff(6193,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6194,plain,
% 2.24/2.40 (~b(z, s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6193, 376, 3686, 3281, 357])).
% 2.24/2.40 tff(6195,plain,
% 2.24/2.40 (r(z, s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[293, 6194])).
% 2.24/2.40 tff(6196,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6197,plain,
% 2.24/2.40 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.40 inference(rewrite,[status(thm)],[])).
% 2.24/2.40 tff(6198,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.40 inference(monotonicity,[status(thm)],[6197])).
% 2.24/2.40 tff(6199,plain,
% 2.24/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.40 inference(transitivity,[status(thm)],[6198, 6196])).
% 2.24/2.40 tff(6200,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.24/2.40 inference(quant_inst,[status(thm)],[])).
% 2.24/2.40 tff(6201,plain,
% 2.24/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.40 inference(modus_ponens,[status(thm)],[6200, 6199])).
% 2.24/2.40 tff(6202,plain,
% 2.24/2.40 (~b(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6201, 171, 3281, 259, 376, 357])).
% 2.24/2.40 tff(6203,plain,
% 2.24/2.40 (r(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[124, 6202])).
% 2.24/2.40 tff(6204,plain,
% 2.24/2.40 ($false),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[526, 106, 6203, 6195, 568, 6185])).
% 2.24/2.40 tff(6205,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(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(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.40 tff(6206,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[6205, 357, 3281, 259, 376])).
% 2.24/2.40 tff(6207,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[3668, 6206])).
% 2.24/2.40 tff(6208,plain,
% 2.24/2.40 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[566, 357, 259, 376])).
% 2.24/2.40 tff(6209,plain,
% 2.24/2.40 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[374, 6208, 355])).
% 2.24/2.40 tff(6210,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[587, 6209, 259, 6207, 554, 357])).
% 2.24/2.40 tff(6211,plain,
% 2.24/2.40 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[205, 6210])).
% 2.24/2.40 tff(6212,plain,
% 2.24/2.40 (~b(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[179, 6211, 159, 1])).
% 2.24/2.40 tff(6213,plain,
% 2.24/2.40 (r(z, s(s(z)))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[124, 6212])).
% 2.24/2.40 tff(6214,plain,
% 2.24/2.40 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.40 inference(unit_resolution,[status(thm)],[608, 6213, 95, 554])).
% 2.24/2.40 tff(6215,plain,
% 2.24/2.41 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[351, 6214])).
% 2.24/2.41 tff(6216,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[597, 171, 259, 376, 357, 6215])).
% 2.24/2.41 tff(6217,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6218,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6217, 6177, 6175, 6161, 95, 554, 5587, 5577, 3281])).
% 2.24/2.41 tff(6219,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6220,plain,
% 2.24/2.41 (~r(s(z), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6219, 502, 3281, 95, 83, 126])).
% 2.24/2.41 tff(6221,plain,
% 2.24/2.41 (b(s(z), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[550, 6220])).
% 2.24/2.41 tff(6222,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6223,plain,
% 2.24/2.41 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6224,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6223])).
% 2.24/2.41 tff(6225,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6224, 6222])).
% 2.24/2.41 tff(6226,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6227,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6226, 6225])).
% 2.24/2.41 tff(6228,plain,
% 2.24/2.41 (~b(z, s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6227, 171, 6221, 3281, 6161])).
% 2.24/2.41 tff(6229,plain,
% 2.24/2.41 (r(z, s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[124, 6228])).
% 2.24/2.41 tff(6230,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6231,plain,
% 2.24/2.41 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6232,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6231])).
% 2.24/2.41 tff(6233,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6232, 6230])).
% 2.24/2.41 tff(6234,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6235,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6234, 6233])).
% 2.24/2.41 tff(6236,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6235, 171, 323, 3281, 259, 1])).
% 2.24/2.41 tff(6237,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6238,plain,
% 2.24/2.41 (~b(s(s(z)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6237, 6221, 3281, 6161])).
% 2.24/2.41 tff(6239,plain,
% 2.24/2.41 (r(s(s(z)), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[157, 6238])).
% 2.24/2.41 tff(6240,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6241,plain,
% 2.24/2.41 (((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6242,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6241])).
% 2.24/2.41 tff(6243,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6242, 6240])).
% 2.24/2.41 tff(6244,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6245,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6244, 6243])).
% 2.24/2.41 tff(6246,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6245, 106, 637, 600, 5567, 569])).
% 2.24/2.41 tff(6247,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6248,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6247, 6239, 6229, 5566])).
% 2.24/2.41 tff(6249,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[374, 6248, 355])).
% 2.24/2.41 tff(6250,plain,
% 2.24/2.41 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[365, 6249, 6161, 6221])).
% 2.24/2.41 tff(6251,plain,
% 2.24/2.41 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[321, 6250, 255])).
% 2.24/2.41 tff(6252,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[4317, 171, 323, 259, 376, 356])).
% 2.24/2.41 tff(6253,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6254,plain,
% 2.24/2.41 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6253, 6249, 6161, 6221])).
% 2.24/2.41 tff(6255,plain,
% 2.24/2.41 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[454, 6254, 254])).
% 2.24/2.41 tff(6256,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6257,plain,
% 2.24/2.41 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6258,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6257])).
% 2.24/2.41 tff(6259,plain,
% 2.24/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6258, 6256])).
% 2.24/2.41 tff(6260,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6261,plain,
% 2.24/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 2.24/2.41 tff(6262,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6261, 106, 95, 5566, 6255, 6251])).
% 2.24/2.41 tff(6263,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6264,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6263, 5531, 31, 83, 61])).
% 2.24/2.41 tff(6265,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[479, 6264])).
% 2.24/2.41 tff(6266,plain,
% 2.24/2.41 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5678, 127, 4, 126])).
% 2.24/2.41 tff(6267,plain,
% 2.24/2.41 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[3668, 6266])).
% 2.24/2.41 tff(6268,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[5548, 6267, 5589, 83, 5598])).
% 2.24/2.41 tff(6269,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6270,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6269, 83, 6265, 61, 31])).
% 2.24/2.41 tff(6271,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[145, 6270])).
% 2.24/2.41 tff(6272,plain,
% 2.24/2.41 (~r(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6159, 83, 31, 5531, 61])).
% 2.24/2.41 tff(6273,plain,
% 2.24/2.41 (b(s(s(z)), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[244, 6272])).
% 2.24/2.41 tff(6274,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6275,plain,
% 2.24/2.41 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(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(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6276,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6275])).
% 2.24/2.41 tff(6277,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6276, 6274])).
% 2.24/2.41 tff(6278,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6279,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.41 inference(modus_ponens,[status(thm)],[6278, 6277])).
% 2.24/2.41 tff(6280,plain,
% 2.24/2.41 ($false),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6279, 171, 323, 3281, 259, 4, 159])).
% 2.24/2.41 tff(6281,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.41 tff(6282,plain,
% 2.24/2.41 (~b(s(z), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6281, 5531, 6273, 6265, 6271])).
% 2.24/2.41 tff(6283,plain,
% 2.24/2.41 (r(s(z), s(s(z)))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[550, 6282])).
% 2.24/2.41 tff(6284,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6263, 3281, 95, 83, 126])).
% 2.24/2.41 tff(6285,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[479, 6284])).
% 2.24/2.41 tff(6286,plain,
% 2.24/2.41 (~r(s(s(s(s(s(z))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[6269, 83, 6285, 126, 95])).
% 2.24/2.41 tff(6287,plain,
% 2.24/2.41 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.41 inference(unit_resolution,[status(thm)],[145, 6286])).
% 2.24/2.41 tff(6288,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6289,plain,
% 2.24/2.41 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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)), s(z))) | (~b(z, 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))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(rewrite,[status(thm)],[])).
% 2.24/2.41 tff(6290,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(z, s(s(s(s(z))))))))),
% 2.24/2.41 inference(monotonicity,[status(thm)],[6289])).
% 2.24/2.41 tff(6291,plain,
% 2.24/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(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(z, s(s(s(s(z)))))))),
% 2.24/2.41 inference(transitivity,[status(thm)],[6290, 6288])).
% 2.24/2.41 tff(6292,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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)))),
% 2.24/2.41 inference(quant_inst,[status(thm)],[])).
% 2.24/2.41 tff(6293,plain,
% 2.24/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6292, 6291])).
% 2.24/2.42 tff(6294,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6293, 171, 3281, 259, 83, 159, 356, 2527])).
% 2.24/2.42 tff(6295,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), 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))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6296,plain,
% 2.24/2.42 (~b(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6295, 356, 259, 83, 159, 3281])).
% 2.24/2.42 tff(6297,plain,
% 2.24/2.42 (r(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[293, 6296])).
% 2.24/2.42 tff(6298,plain,
% 2.24/2.42 (~r(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5575, 6297, 95, 554])).
% 2.24/2.42 tff(6299,plain,
% 2.24/2.42 (b(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[157, 6298])).
% 2.24/2.42 tff(6300,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6301,plain,
% 2.24/2.42 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), 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(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6302,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6301])).
% 2.24/2.42 tff(6303,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6302, 6300])).
% 2.24/2.42 tff(6304,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6305,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6304, 6303])).
% 2.24/2.42 tff(6306,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6305, 171, 259, 161, 1, 356, 2141])).
% 2.24/2.42 tff(6307,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6308,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6307, 6299, 161, 356, 259])).
% 2.24/2.42 tff(6309,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[274, 6308])).
% 2.24/2.42 tff(6310,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6311,plain,
% 2.24/2.42 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6312,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6311])).
% 2.24/2.42 tff(6313,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6312, 6310])).
% 2.24/2.42 tff(6314,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6315,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6314, 6313])).
% 2.24/2.42 tff(6316,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6315, 106, 95, 6297, 3, 6309])).
% 2.24/2.42 tff(6317,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(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(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6318,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6317, 3, 95, 161, 6161, 554, 83, 6287, 3281])).
% 2.24/2.42 tff(6319,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[374, 6318, 355])).
% 2.24/2.42 tff(6320,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6321,plain,
% 2.24/2.42 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6322,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6321])).
% 2.24/2.42 tff(6323,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6322, 6320])).
% 2.24/2.42 tff(6324,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6325,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6324, 6323])).
% 2.24/2.42 tff(6326,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6325, 106, 95, 5567, 3, 569])).
% 2.24/2.42 tff(6327,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6328,plain,
% 2.24/2.42 (~r(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6327, 3, 95, 6319])).
% 2.24/2.42 tff(6329,plain,
% 2.24/2.42 (b(z, s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[293, 6328])).
% 2.24/2.42 tff(6330,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3187, 106, 95, 126, 396, 1288])).
% 2.24/2.42 tff(6331,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6332,plain,
% 2.24/2.42 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6331, 396, 126, 95])).
% 2.24/2.42 tff(6333,plain,
% 2.24/2.42 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[498, 6332])).
% 2.24/2.42 tff(6334,plain,
% 2.24/2.42 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[463, 396, 126, 3])).
% 2.24/2.42 tff(6335,plain,
% 2.24/2.42 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3668, 6334])).
% 2.24/2.42 tff(6336,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5548, 6335, 6333, 83, 2527])).
% 2.24/2.42 tff(6337,plain,((~r(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)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6338,plain,
% 2.24/2.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6337, 6329, 83, 126, 3, 95])).
% 2.24/2.42 tff(6339,plain,
% 2.24/2.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[225, 6338])).
% 2.24/2.42 tff(6340,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(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(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(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(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6341,plain,
% 2.24/2.42 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(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(z, s(z))) | (~b(z, 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(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6342,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(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(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6341])).
% 2.24/2.42 tff(6343,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(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(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6342, 6340])).
% 2.24/2.42 tff(6344,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(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)))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6345,plain,
% 2.24/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6344, 6343])).
% 2.24/2.42 tff(6346,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6345, 171, 3281, 161, 4, 160, 207, 159])).
% 2.24/2.42 tff(6347,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6348,plain,
% 2.24/2.42 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6347, 6339, 3281, 6285, 6287, 161])).
% 2.24/2.42 tff(6349,plain,
% 2.24/2.42 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[205, 6348])).
% 2.24/2.42 tff(6350,plain,
% 2.24/2.42 (~b(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[215, 6339, 6287, 161])).
% 2.24/2.42 tff(6351,plain,
% 2.24/2.42 (r(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[157, 6350])).
% 2.24/2.42 tff(6352,plain,
% 2.24/2.42 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5959, 6351, 554, 95])).
% 2.24/2.42 tff(6353,plain,
% 2.24/2.42 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[498, 6352])).
% 2.24/2.42 tff(6354,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5548, 6353, 83, 6329])).
% 2.24/2.42 tff(6355,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[3668, 6354])).
% 2.24/2.42 tff(6356,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[587, 6355, 6161, 6319, 554, 6349])).
% 2.24/2.42 tff(6357,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[321, 6356, 255])).
% 2.24/2.42 tff(6358,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6359,plain,
% 2.24/2.42 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.42 inference(rewrite,[status(thm)],[])).
% 2.24/2.42 tff(6360,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.24/2.42 inference(monotonicity,[status(thm)],[6359])).
% 2.24/2.42 tff(6361,plain,
% 2.24/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.42 inference(transitivity,[status(thm)],[6360, 6358])).
% 2.24/2.42 tff(6362,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.24/2.42 inference(quant_inst,[status(thm)],[])).
% 2.24/2.42 tff(6363,plain,
% 2.24/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.24/2.42 inference(modus_ponens,[status(thm)],[6362, 6361])).
% 2.24/2.42 tff(6364,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6363, 106, 554, 6351, 6357, 6319])).
% 2.24/2.42 tff(6365,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6366,plain,
% 2.24/2.42 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6365, 554, 83, 95, 3281, 161, 126])).
% 2.24/2.42 tff(6367,plain,
% 2.24/2.42 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[454, 6366, 254])).
% 2.24/2.42 tff(6368,plain,
% 2.24/2.42 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[445, 6367, 6161, 6285])).
% 2.24/2.42 tff(6369,plain,
% 2.24/2.42 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[321, 6368, 255])).
% 2.24/2.42 tff(6370,plain,
% 2.24/2.42 (~r(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[5959, 1288, 554, 95])).
% 2.24/2.42 tff(6371,plain,
% 2.24/2.42 (b(s(s(z)), z)),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[157, 6370])).
% 2.24/2.42 tff(6372,plain,
% 2.24/2.42 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6331, 1288, 126, 95])).
% 2.24/2.42 tff(6373,plain,
% 2.24/2.42 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[225, 6372])).
% 2.24/2.42 tff(6374,plain,
% 2.24/2.42 ($false),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[215, 6373, 6371, 159, 161])).
% 2.24/2.42 tff(6375,plain,((~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.42 tff(6376,plain,
% 2.24/2.42 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[6375, 554, 161, 126, 95, 6287])).
% 2.24/2.42 tff(6377,plain,
% 2.24/2.42 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.42 inference(unit_resolution,[status(thm)],[498, 6376])).
% 2.24/2.42 tff(6378,plain,
% 2.24/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6379,plain,
% 2.24/2.43 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(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(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6380,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6379])).
% 2.24/2.43 tff(6381,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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)))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6380, 6378])).
% 2.24/2.43 tff(6382,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), 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))))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6383,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(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))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6382, 6381])).
% 2.24/2.43 tff(6384,plain,
% 2.24/2.43 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6383, 171, 6161, 161, 83, 6367])).
% 2.24/2.43 tff(6385,plain,
% 2.24/2.43 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6384, 6377])).
% 2.24/2.43 tff(6386,plain,
% 2.24/2.43 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[225, 6385])).
% 2.24/2.43 tff(6387,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6388,plain,
% 2.24/2.43 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6389,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6388])).
% 2.24/2.43 tff(6390,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6389, 6387])).
% 2.24/2.43 tff(6391,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6392,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6391, 6390])).
% 2.24/2.43 tff(6393,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6392, 171, 3686, 83, 4, 376])).
% 2.24/2.43 tff(6394,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6395,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6394, 6367, 83, 6285])).
% 2.24/2.43 tff(6396,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3668, 6395])).
% 2.24/2.43 tff(6397,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6398,plain,
% 2.24/2.43 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6399,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6398])).
% 2.24/2.43 tff(6400,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6399, 6397])).
% 2.24/2.43 tff(6401,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(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(z))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6402,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6401, 6400])).
% 2.24/2.43 tff(6403,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6402, 106, 6396, 126, 6386, 6369])).
% 2.24/2.43 tff(6404,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6405,plain,
% 2.24/2.43 (~b(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6404, 6283, 61, 83, 31, 5531])).
% 2.24/2.43 tff(6406,plain,
% 2.24/2.43 (r(z, s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[124, 6405])).
% 2.24/2.43 tff(6407,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2686, 6406, 6283, 31])).
% 2.24/2.43 tff(6408,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[608, 6406, 31, 6283])).
% 2.24/2.43 tff(6409,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[351, 6408])).
% 2.24/2.43 tff(6410,plain,
% 2.24/2.43 (~r(s(s(z)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[2952, 6406, 6283, 31])).
% 2.24/2.43 tff(6411,plain,
% 2.24/2.43 (b(s(s(z)), z)),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[157, 6410])).
% 2.24/2.43 tff(6412,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6413,plain,
% 2.24/2.43 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6414,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6413])).
% 2.24/2.43 tff(6415,plain,
% 2.24/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6414, 6412])).
% 2.24/2.43 tff(6416,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6417,plain,
% 2.24/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6416, 6415])).
% 2.24/2.43 tff(6418,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6417, 106, 554, 95, 600, 501])).
% 2.24/2.43 tff(6419,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6420,plain,
% 2.24/2.43 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6419, 6283, 31, 6406])).
% 2.24/2.43 tff(6421,plain,
% 2.24/2.43 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[205, 6420])).
% 2.24/2.43 tff(6422,plain,
% 2.24/2.43 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[4606, 6421, 83, 31, 6271, 6283, 6411])).
% 2.24/2.43 tff(6423,plain,
% 2.24/2.43 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[3668, 6422])).
% 2.24/2.43 tff(6424,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(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(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(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(z))))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6425,plain,
% 2.24/2.43 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(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(s(s(s(z))))), z)))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6426,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(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(z))))), z))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6425])).
% 2.24/2.43 tff(6427,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(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(z))))), z)))),
% 2.24/2.43 inference(transitivity,[status(thm)],[6426, 6424])).
% 2.24/2.43 tff(6428,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.43 inference(quant_inst,[status(thm)],[])).
% 2.24/2.43 tff(6429,plain,
% 2.24/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.43 inference(modus_ponens,[status(thm)],[6428, 6427])).
% 2.24/2.43 tff(6430,plain,
% 2.24/2.43 ($false),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6429, 171, 3281, 1, 83, 376, 160, 159])).
% 2.24/2.43 tff(6431,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.43 tff(6432,plain,
% 2.24/2.43 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6431, 6421, 6411, 83, 5531, 6271])).
% 2.24/2.43 tff(6433,plain,
% 2.24/2.43 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[454, 6432, 254])).
% 2.24/2.43 tff(6434,plain,
% 2.24/2.43 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[463, 6433, 61, 6423])).
% 2.24/2.43 tff(6435,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[225, 6434])).
% 2.24/2.43 tff(6436,plain,
% 2.24/2.43 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1365, 6423, 61, 6433])).
% 2.24/2.43 tff(6437,plain,
% 2.24/2.43 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[1368, 6436])).
% 2.24/2.43 tff(6438,plain,
% 2.24/2.43 (~r(z, s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[6081, 6433, 31, 6423])).
% 2.24/2.43 tff(6439,plain,
% 2.24/2.43 (b(z, s(s(s(s(z)))))),
% 2.24/2.43 inference(unit_resolution,[status(thm)],[293, 6438])).
% 2.24/2.43 tff(6440,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6441,plain,
% 2.24/2.43 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.43 inference(rewrite,[status(thm)],[])).
% 2.24/2.43 tff(6442,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.24/2.43 inference(monotonicity,[status(thm)],[6441])).
% 2.24/2.43 tff(6443,plain,
% 2.24/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6442, 6440])).
% 2.24/2.44 tff(6444,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6445,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6444, 6443])).
% 2.24/2.44 tff(6446,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6445, 171, 1, 4, 160, 159, 357, 2527])).
% 2.24/2.44 tff(6447,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6448,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6447, 6411, 6265, 6421, 6271, 6439])).
% 2.24/2.44 tff(6449,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[321, 6448, 255])).
% 2.24/2.44 tff(6450,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6451,plain,
% 2.24/2.44 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6452,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6451])).
% 2.24/2.44 tff(6453,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6452, 6450])).
% 2.24/2.44 tff(6454,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6455,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6454, 6453])).
% 2.24/2.44 tff(6456,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6455, 171, 3281, 1, 1976, 1384, 160, 159])).
% 2.24/2.44 tff(6457,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6458,plain,
% 2.24/2.44 (~b(s(z), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6457, 5531, 6411, 6437, 6421, 6271])).
% 2.24/2.44 tff(6459,plain,
% 2.24/2.44 (r(s(z), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[1996, 6458])).
% 2.24/2.44 tff(6460,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2126, 6449, 31, 6406])).
% 2.24/2.44 tff(6461,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[274, 6460])).
% 2.24/2.44 tff(6462,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.44 tff(6463,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6464,plain,
% 2.24/2.44 (((~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(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(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)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6465,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6464])).
% 2.24/2.44 tff(6466,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6465, 6463])).
% 2.24/2.44 tff(6467,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6468,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6467, 6466])).
% 2.24/2.44 tff(6469,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6468, 171, 1, 6462, 2527, 2352, 2141])).
% 2.24/2.44 tff(6470,plain,((~b(s(s(s(s(z)))), 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)))))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6471,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6470, 6411, 6439, 6409, 6461])).
% 2.24/2.44 tff(6472,assumption,(~b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.44 tff(6473,assumption,(~r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.44 tff(6474,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[4240, 25, 6473, 6472, 4230])).
% 2.24/2.44 tff(6475,plain,(r(s(s(s(s(z)))), s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6476,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6475, 6471])).
% 2.24/2.44 tff(6477,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.24/2.44 tff(6478,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6479,plain,
% 2.24/2.44 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6480,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6479])).
% 2.24/2.44 tff(6481,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6480, 6478])).
% 2.24/2.44 tff(6482,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6483,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6482, 6481])).
% 2.24/2.44 tff(6484,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6483, 106, 2604, 1998, 6477, 263])).
% 2.24/2.44 tff(6485,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6486,plain,
% 2.24/2.44 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6485, 6476, 6459, 6449])).
% 2.24/2.44 tff(6487,plain,
% 2.24/2.44 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[2614, 6486])).
% 2.24/2.44 tff(6488,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6489,plain,
% 2.24/2.44 (((~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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(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(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6490,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.24/2.44 inference(monotonicity,[status(thm)],[6489])).
% 2.24/2.44 tff(6491,plain,
% 2.24/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.44 inference(transitivity,[status(thm)],[6490, 6488])).
% 2.24/2.44 tff(6492,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6493,plain,
% 2.24/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6492, 6491])).
% 2.24/2.44 tff(6494,plain,
% 2.24/2.44 (~b(s(s(z)), s(s(s(z))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6493, 171, 83, 6487, 6437, 6435, 6409])).
% 2.24/2.44 tff(6495,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[979, 25, 6494, 6407, 82])).
% 2.24/2.44 tff(6496,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6497,plain,
% 2.24/2.44 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6496, 32, 5])).
% 2.24/2.44 tff(6498,plain,
% 2.24/2.44 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[427, 6497])).
% 2.24/2.44 tff(6499,assumption,(~r(s(z), s(s(z)))), introduced(assumption)).
% 2.24/2.44 tff(6500,plain,
% 2.24/2.44 (b(s(z), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[550, 6499])).
% 2.24/2.44 tff(6501,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[135, 94, 95, 61])).
% 2.24/2.44 tff(6502,plain,
% 2.24/2.44 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[145, 6501])).
% 2.24/2.44 tff(6503,plain,
% 2.24/2.44 (~r(s(z), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5186, 637, 94, 95])).
% 2.24/2.44 tff(6504,plain,
% 2.24/2.44 (b(s(z), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[550, 6503])).
% 2.24/2.44 tff(6505,plain,
% 2.24/2.44 (~r(s(s(z)), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[234, 94, 61, 95])).
% 2.24/2.44 tff(6506,plain,
% 2.24/2.44 (b(s(s(z)), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[244, 6505])).
% 2.24/2.44 tff(6507,plain,
% 2.24/2.44 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[5539, 5277, 61, 95])).
% 2.24/2.44 tff(6508,plain,
% 2.24/2.44 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[498, 6507])).
% 2.24/2.44 tff(6509,plain,
% 2.24/2.44 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[3978, 6508, 95, 94, 5277])).
% 2.24/2.44 tff(6510,plain,
% 2.24/2.44 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[321, 6509, 255])).
% 2.24/2.44 tff(6511,plain,
% 2.24/2.44 ($false),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[329, 171, 323, 259, 357, 2352])).
% 2.24/2.44 tff(6512,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.44 tff(6513,plain,
% 2.24/2.44 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6512, 6510, 6506, 6504])).
% 2.24/2.44 tff(6514,plain,
% 2.24/2.44 (r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[351, 6513])).
% 2.24/2.44 tff(6515,plain,
% 2.24/2.44 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[365, 6510, 6506, 6504])).
% 2.24/2.44 tff(6516,plain,
% 2.24/2.44 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[374, 6515, 355])).
% 2.24/2.44 tff(6517,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.44 inference(rewrite,[status(thm)],[])).
% 2.24/2.44 tff(6518,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.24/2.44 inference(quant_inst,[status(thm)],[])).
% 2.24/2.44 tff(6519,plain,
% 2.24/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.24/2.44 inference(modus_ponens,[status(thm)],[6518, 6517])).
% 2.24/2.44 tff(6520,plain,
% 2.24/2.44 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.44 inference(unit_resolution,[status(thm)],[6519, 106, 5609, 6516, 6514])).
% 2.24/2.44 tff(6521,plain,
% 2.24/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6522,plain,
% 2.24/2.45 (((~r(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(z)), 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(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6523,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6522])).
% 2.24/2.45 tff(6524,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6523, 6521])).
% 2.24/2.45 tff(6525,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6526,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6525, 6524])).
% 2.24/2.45 tff(6527,plain,
% 2.24/2.45 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6526, 106, 5609, 6516, 6514])).
% 2.24/2.45 tff(6528,plain,
% 2.24/2.45 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[205, 6527])).
% 2.24/2.45 tff(6529,plain,
% 2.24/2.45 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[225, 219])).
% 2.24/2.45 tff(6530,plain,
% 2.24/2.45 (~r(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[234, 96, 61, 95])).
% 2.24/2.45 tff(6531,plain,
% 2.24/2.45 (b(s(s(z)), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[244, 6530])).
% 2.24/2.45 tff(6532,plain,
% 2.24/2.45 (~r(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[135, 96, 95, 61])).
% 2.24/2.45 tff(6533,plain,
% 2.24/2.45 (b(s(s(s(s(s(z))))), z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[145, 6532])).
% 2.24/2.45 tff(6534,plain,
% 2.24/2.45 (~r(s(z), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5186, 637, 96, 95])).
% 2.24/2.45 tff(6535,plain,
% 2.24/2.45 (b(s(z), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[550, 6534])).
% 2.24/2.45 tff(6536,plain,
% 2.24/2.45 (~b(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5201, 207, 6531, 6535, 6533])).
% 2.24/2.45 tff(6537,plain,
% 2.24/2.45 (r(z, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[124, 6536])).
% 2.24/2.45 tff(6538,plain,
% 2.24/2.45 (~(s(z) = elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1439, 1437])).
% 2.24/2.45 tff(6539,plain,
% 2.24/2.45 (b(s(z), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1444, 1924, 6538])).
% 2.24/2.45 tff(6540,plain,
% 2.24/2.45 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3725, 6539, 32])).
% 2.24/2.45 tff(6541,plain,
% 2.24/2.45 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[5539, 502, 61, 95])).
% 2.24/2.45 tff(6542,plain,
% 2.24/2.45 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[498, 6541])).
% 2.24/2.45 tff(6543,plain,
% 2.24/2.45 (~(z = elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1927, 1924, 95])).
% 2.24/2.45 tff(6544,plain,
% 2.24/2.45 (~(elem!1 = z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[697, 6543])).
% 2.24/2.45 tff(6545,plain,
% 2.24/2.45 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[777, 730, 95, 502])).
% 2.24/2.45 tff(6546,plain,
% 2.24/2.45 (b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[782, 6545, 1908])).
% 2.24/2.45 tff(6547,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6548,plain,
% 2.24/2.45 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6549,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6548])).
% 2.24/2.45 tff(6550,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6549, 6547])).
% 2.24/2.45 tff(6551,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6552,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6551, 6550])).
% 2.24/2.45 tff(6553,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6552, 106, 1554, 730, 95, 600])).
% 2.24/2.45 tff(6554,plain,((~r(elem!1, z)) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6555,plain,
% 2.24/2.45 (~r(elem!1, z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6554, 730, 95, 600])).
% 2.24/2.45 tff(6556,plain,
% 2.24/2.45 (b(elem!1, z)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1567, 6555, 3385])).
% 2.24/2.45 tff(6557,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6558,plain,
% 2.24/2.45 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(elem!1, 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))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6559,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, 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))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6558])).
% 2.24/2.45 tff(6560,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, 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))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6559, 6557])).
% 2.24/2.45 tff(6561,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6562,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6561, 6560])).
% 2.24/2.45 tff(6563,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6562, 171, 6556, 6546, 160, 207, 1313])).
% 2.24/2.45 tff(6564,plain,((~r(elem!1, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (elem!1 = z) | (elem!1 = s(s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6565,plain,
% 2.24/2.45 (~r(elem!1, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6564, 6544, 207, 6542, 160, 6540, 95, 6537, 502])).
% 2.24/2.45 tff(6566,plain,
% 2.24/2.45 (b(elem!1, s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[687, 6565, 1437])).
% 2.24/2.45 tff(6567,plain,
% 2.24/2.45 (~b(elem!1, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3733, 171, 6535, 6566, 6531])).
% 2.24/2.45 tff(6568,plain,
% 2.24/2.45 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3978, 6542, 95, 96, 502])).
% 2.24/2.45 tff(6569,plain,
% 2.24/2.45 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[321, 6568, 255])).
% 2.24/2.45 tff(6570,plain,
% 2.24/2.45 (~b(s(s(z)), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3074, 6565, 6531, 6538, 1924])).
% 2.24/2.45 tff(6571,plain,
% 2.24/2.45 (~(s(elem!1) = s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[922, 6543])).
% 2.24/2.45 tff(6572,plain,
% 2.24/2.45 (s(s(z)) = elem!1),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3750, 638, 637, 3741, 733])).
% 2.24/2.45 tff(6573,plain,
% 2.24/2.45 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1613, 6572, 701])).
% 2.24/2.45 tff(6574,plain,
% 2.24/2.45 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1620, 6573])).
% 2.24/2.45 tff(6575,plain,
% 2.24/2.45 (s(s(s(z))) = s(elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6572])).
% 2.24/2.45 tff(6576,plain,
% 2.24/2.45 (r(s(s(s(z))), s(z)) <=> r(s(elem!1), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6575])).
% 2.24/2.45 tff(6577,plain,
% 2.24/2.45 (~b(s(s(s(z))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[2702, 638, 259, 637, 357, 95])).
% 2.24/2.45 tff(6578,plain,
% 2.24/2.45 (r(s(s(s(z))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1173, 6577])).
% 2.24/2.45 tff(6579,plain,
% 2.24/2.45 (r(s(elem!1), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6578, 6576])).
% 2.24/2.45 tff(6580,plain,
% 2.24/2.45 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6575])).
% 2.24/2.45 tff(6581,plain,
% 2.24/2.45 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6580])).
% 2.24/2.45 tff(6582,plain,
% 2.24/2.45 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6581])).
% 2.24/2.45 tff(6583,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[502, 6582])).
% 2.24/2.45 tff(6584,plain,
% 2.24/2.45 ($false),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1712, 6583, 6579, 95, 96, 6574])).
% 2.24/2.45 tff(6585,plain,((~r(z, elem!1)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(z)), z)) | b(elem!1, s(s(z))) | b(s(s(z)), elem!1) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.45 tff(6586,plain,
% 2.24/2.45 (~r(z, elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6585, 6571, 96, 502, 95, 637, 6567, 6570, 6531, 6569])).
% 2.24/2.45 tff(6587,plain,
% 2.24/2.45 (b(z, elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[651, 6586, 6543])).
% 2.24/2.45 tff(6588,plain,
% 2.24/2.45 (~(s(s(z)) = elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[4910, 6587, 6536])).
% 2.24/2.45 tff(6589,plain,
% 2.24/2.45 (~(elem!1 = s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3737, 6588])).
% 2.24/2.45 tff(6590,plain,
% 2.24/2.45 (r(elem!1, s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3154, 6589, 6567])).
% 2.24/2.45 tff(6591,plain,
% 2.24/2.45 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[365, 6569, 6531, 6535])).
% 2.24/2.45 tff(6592,plain,
% 2.24/2.45 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[374, 6591, 355])).
% 2.24/2.45 tff(6593,plain,
% 2.24/2.45 (r(s(s(z)), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1416, 6588, 6570])).
% 2.24/2.45 tff(6594,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6595,plain,
% 2.24/2.45 (((~r(s(s(z)), elem!1)) | (~r(elem!1, 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(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6596,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6595])).
% 2.24/2.45 tff(6597,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6596, 6594])).
% 2.24/2.45 tff(6598,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6599,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6598, 6597])).
% 2.24/2.45 tff(6600,plain,
% 2.24/2.45 (~r(s(s(s(s(z)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6599, 106, 6590, 6593, 6592])).
% 2.24/2.45 tff(6601,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6602,plain,
% 2.24/2.45 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6603,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6602])).
% 2.24/2.45 tff(6604,plain,
% 2.24/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6603, 6601])).
% 2.24/2.45 tff(6605,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6606,plain,
% 2.24/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z)))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6605, 6604])).
% 2.24/2.45 tff(6607,plain,
% 2.24/2.45 (~b(s(s(s(s(z)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6606, 171, 6566, 6539, 6569])).
% 2.24/2.45 tff(6608,plain,
% 2.24/2.45 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3814, 25, 6607])).
% 2.24/2.45 tff(6609,plain,
% 2.24/2.45 (s(s(s(s(z)))) = elem!1),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6608, 6600])).
% 2.24/2.45 tff(6610,plain,
% 2.24/2.45 (s(s(s(s(s(z))))) = s(elem!1)),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6609])).
% 2.24/2.45 tff(6611,plain,
% 2.24/2.45 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6610])).
% 2.24/2.45 tff(6612,plain,
% 2.24/2.45 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6611, 1615])).
% 2.24/2.45 tff(6613,plain,
% 2.24/2.45 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6612, 3740])).
% 2.24/2.45 tff(6614,plain,
% 2.24/2.45 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(s(elem!1)))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6613])).
% 2.24/2.45 tff(6615,plain,
% 2.24/2.45 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3828, 6588])).
% 2.24/2.45 tff(6616,plain,
% 2.24/2.45 (~(s(elem!1) = s(s(s(elem!1))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6615, 6614])).
% 2.24/2.45 tff(6617,plain,
% 2.24/2.45 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(elem!1), s(z))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6610])).
% 2.24/2.45 tff(6618,plain,
% 2.24/2.45 (r(s(elem!1), s(z))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[502, 6617])).
% 2.24/2.45 tff(6619,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1712, 6618, 95, 96, 6616])).
% 2.24/2.45 tff(6620,plain,
% 2.24/2.45 (b(s(s(s(elem!1))), s(z))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1807, 6619])).
% 2.24/2.45 tff(6621,plain,
% 2.24/2.45 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3840, 171, 6535, 6620, 6531])).
% 2.24/2.45 tff(6622,plain,
% 2.24/2.45 (r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1013, 6621])).
% 2.24/2.45 tff(6623,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6624,plain,
% 2.24/2.45 (((~r(s(s(z)), z)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.24/2.45 inference(rewrite,[status(thm)],[])).
% 2.24/2.45 tff(6625,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6624])).
% 2.24/2.45 tff(6626,plain,
% 2.24/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6625, 6623])).
% 2.24/2.45 tff(6627,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.24/2.45 inference(quant_inst,[status(thm)],[])).
% 2.24/2.45 tff(6628,plain,
% 2.24/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.24/2.45 inference(modus_ponens,[status(thm)],[6627, 6626])).
% 2.24/2.45 tff(6629,plain,
% 2.24/2.45 (~r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6628, 106, 6622, 6590, 637])).
% 2.24/2.45 tff(6630,plain,
% 2.24/2.45 (~b(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3855, 171, 6535, 6620, 6566, 6531])).
% 2.24/2.45 tff(6631,plain,
% 2.24/2.45 ((s(s(s(elem!1))) = elem!1) | r(s(s(s(elem!1))), elem!1)),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[3859, 25, 6630])).
% 2.24/2.45 tff(6632,plain,
% 2.24/2.45 (s(s(s(elem!1))) = elem!1),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[6631, 6629])).
% 2.24/2.45 tff(6633,plain,
% 2.24/2.45 (elem!1 = s(s(s(elem!1)))),
% 2.24/2.45 inference(symmetry,[status(thm)],[6632])).
% 2.24/2.45 tff(6634,plain,
% 2.24/2.45 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.24/2.45 inference(transitivity,[status(thm)],[6609, 6633])).
% 2.24/2.45 tff(6635,plain,
% 2.24/2.45 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6634])).
% 2.24/2.45 tff(6636,plain,
% 2.24/2.45 (s(s(s(z))) = s(s(elem!1))),
% 2.24/2.45 inference(transitivity,[status(thm)],[191, 6635, 812])).
% 2.24/2.45 tff(6637,plain,
% 2.24/2.45 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 2.24/2.45 inference(monotonicity,[status(thm)],[6636])).
% 2.24/2.45 tff(6638,plain,
% 2.24/2.45 (s(s(z)) = s(elem!1)),
% 2.24/2.45 inference(transitivity,[status(thm)],[341, 6637, 1002])).
% 2.24/2.45 tff(6639,plain,
% 2.24/2.45 (~(s(s(z)) = s(elem!1))),
% 2.24/2.45 inference(unit_resolution,[status(thm)],[1551, 1437])).
% 2.24/2.45 tff(6640,plain,
% 2.24/2.45 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6639, 6638])).
% 2.24/2.46 tff(6641,plain,(r(s(z), elem!1) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6642,plain,
% 2.24/2.46 (r(s(z), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6641, 1437, 95, 94, 5277, 637, 6529, 160, 32])).
% 2.24/2.46 tff(6643,plain,
% 2.24/2.46 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5539, 5277, 126, 95])).
% 2.24/2.46 tff(6644,plain,
% 2.24/2.46 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[498, 6643])).
% 2.24/2.46 tff(6645,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3978, 6644, 95, 94, 5277])).
% 2.24/2.46 tff(6646,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[321, 6645, 255])).
% 2.24/2.46 tff(6647,plain,
% 2.24/2.46 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[365, 6646, 4905, 6504])).
% 2.24/2.46 tff(6648,plain,
% 2.24/2.46 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[374, 6647, 355])).
% 2.24/2.46 tff(6649,plain,
% 2.24/2.46 (~b(z, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5201, 6529, 4905, 6504, 4903])).
% 2.24/2.46 tff(6650,plain,
% 2.24/2.46 (r(z, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[124, 6649])).
% 2.24/2.46 tff(6651,plain,
% 2.24/2.46 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1890, 666, 6529, 160])).
% 2.24/2.46 tff(6652,plain,
% 2.24/2.46 (~b(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4060, 666, 259, 323])).
% 2.24/2.46 tff(6653,plain,
% 2.24/2.46 (r(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[687, 6652, 1437])).
% 2.24/2.46 tff(6654,plain,
% 2.24/2.46 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[777, 6653, 95, 502])).
% 2.24/2.46 tff(6655,plain,
% 2.24/2.46 (elem!1 = s(s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[782, 6654, 6651])).
% 2.24/2.46 tff(6656,plain,
% 2.24/2.46 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6655])).
% 2.24/2.46 tff(6657,plain,
% 2.24/2.46 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6656])).
% 2.24/2.46 tff(6658,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3707, 600, 637, 569])).
% 2.24/2.46 tff(6659,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[274, 6658])).
% 2.24/2.46 tff(6660,plain,
% 2.24/2.46 (~r(elem!1, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3449, 6655, 219])).
% 2.24/2.46 tff(6661,plain,
% 2.24/2.46 (b(elem!1, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3154, 6660, 3122])).
% 2.24/2.46 tff(6662,plain,
% 2.24/2.46 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.24/2.46 inference(commutativity,[status(thm)],[])).
% 2.24/2.46 tff(6663,plain,
% 2.24/2.46 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6655])).
% 2.24/2.46 tff(6664,plain,
% 2.24/2.46 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6663, 6662])).
% 2.24/2.46 tff(6665,plain,
% 2.24/2.46 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.46 inference(symmetry,[status(thm)],[6664])).
% 2.24/2.46 tff(6666,plain,
% 2.24/2.46 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6665])).
% 2.24/2.46 tff(6667,plain,
% 2.24/2.46 (~(s(s(s(elem!1))) = elem!1)),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[1300, 6666])).
% 2.24/2.46 tff(6668,plain,
% 2.24/2.46 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4474, 6667, 259, 323, 6653, 6661])).
% 2.24/2.46 tff(6669,plain,
% 2.24/2.46 (r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1013, 6668])).
% 2.24/2.46 tff(6670,plain,
% 2.24/2.46 (~r(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5064, 106, 6669, 637, 600])).
% 2.24/2.46 tff(6671,plain,
% 2.24/2.46 (b(s(s(s(elem!1))), z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3048, 6670])).
% 2.24/2.46 tff(6672,plain,
% 2.24/2.46 (~r(z, s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5072, 106, 6669, 637, 600])).
% 2.24/2.46 tff(6673,plain,
% 2.24/2.46 (b(z, s(s(s(elem!1))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1593, 25, 6672, 3930])).
% 2.24/2.46 tff(6674,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6675,plain,
% 2.24/2.46 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6676,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6675])).
% 2.24/2.46 tff(6677,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6676, 6674])).
% 2.24/2.46 tff(6678,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~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)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6679,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6678, 6677])).
% 2.24/2.46 tff(6680,plain,
% 2.24/2.46 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6679, 171, 6673, 6671, 6659])).
% 2.24/2.46 tff(6681,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6682,plain,
% 2.24/2.46 (((~r(s(s(z)), z)) | (~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(z)), 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)))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6683,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6682])).
% 2.24/2.46 tff(6684,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6683, 6681])).
% 2.24/2.46 tff(6685,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~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)))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6686,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6685, 6684])).
% 2.24/2.46 tff(6687,plain,
% 2.24/2.46 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6686, 106, 6669, 637, 569])).
% 2.24/2.46 tff(6688,plain,
% 2.24/2.46 (((~![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))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6689,plain,
% 2.24/2.46 ((~![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))))))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6690,plain,
% 2.24/2.46 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6689, 6688])).
% 2.24/2.46 tff(6691,plain,
% 2.24/2.46 ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6690, 25, 6687])).
% 2.24/2.46 tff(6692,plain,
% 2.24/2.46 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6691, 6680])).
% 2.24/2.46 tff(6693,plain,
% 2.24/2.46 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.24/2.46 inference(symmetry,[status(thm)],[6692])).
% 2.24/2.46 tff(6694,plain,
% 2.24/2.46 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6693])).
% 2.24/2.46 tff(6695,plain,
% 2.24/2.46 (s(s(s(z))) = s(s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[191, 6694, 812, 6657])).
% 2.24/2.46 tff(6696,plain,
% 2.24/2.46 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6695])).
% 2.24/2.46 tff(6697,plain,
% 2.24/2.46 (s(s(z)) = s(s(s(s(s(s(z))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[341, 6696, 3269])).
% 2.24/2.46 tff(6698,plain,
% 2.24/2.46 (~(s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3476, 6655])).
% 2.24/2.46 tff(6699,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6698, 6697])).
% 2.24/2.46 tff(6700,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (elem!1 = s(s(z))) | r(s(s(s(s(s(z))))), s(s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6701,plain,
% 2.24/2.46 (~b(s(s(z)), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6700, 3829, 6650, 6648, 4905, 6504, 637, 3738, 219, 95, 5277, 1437, 160])).
% 2.24/2.46 tff(6702,plain,
% 2.24/2.46 (~b(z, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[5201, 207, 4905, 6504, 4903])).
% 2.24/2.46 tff(6703,plain,
% 2.24/2.46 (r(z, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[124, 6702])).
% 2.24/2.46 tff(6704,plain,
% 2.24/2.46 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3978, 5541, 95, 94, 502])).
% 2.24/2.46 tff(6705,plain,
% 2.24/2.46 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[321, 6704, 255])).
% 2.24/2.46 tff(6706,plain,
% 2.24/2.46 (b(elem!1, s(z))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[687, 676, 1437])).
% 2.24/2.46 tff(6707,plain,
% 2.24/2.46 (~b(elem!1, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3733, 171, 323, 6706, 259])).
% 2.24/2.46 tff(6708,plain,
% 2.24/2.46 (r(elem!1, s(s(z)))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3154, 6707, 3738])).
% 2.24/2.46 tff(6709,plain,
% 2.24/2.46 (~r(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[4988, 6708, 94, 637])).
% 2.24/2.46 tff(6710,plain,
% 2.24/2.46 (b(elem!1, z)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1567, 6709, 1553])).
% 2.24/2.46 tff(6711,plain,
% 2.24/2.46 (~r(z, elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[3750, 6707, 637, 2116, 733])).
% 2.24/2.46 tff(6712,plain,
% 2.24/2.46 (b(z, elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[651, 6711, 1464])).
% 2.24/2.46 tff(6713,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6714,plain,
% 2.24/2.46 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1))) <=> ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6715,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6714])).
% 2.24/2.46 tff(6716,plain,
% 2.24/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6715, 6713])).
% 2.24/2.46 tff(6717,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, elem!1)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6718,plain,
% 2.24/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6717, 6716])).
% 2.24/2.46 tff(6719,plain,
% 2.24/2.46 ((~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6718, 171, 6706, 259, 207, 1313])).
% 2.24/2.46 tff(6720,plain,
% 2.24/2.46 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6719, 6712])).
% 2.24/2.46 tff(6721,assumption,(~b(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 2.24/2.46 tff(6722,plain,
% 2.24/2.46 (r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[782, 1908, 6721])).
% 2.24/2.46 tff(6723,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6724,plain,
% 2.24/2.46 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(rewrite,[status(thm)],[])).
% 2.24/2.46 tff(6725,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.46 inference(monotonicity,[status(thm)],[6724])).
% 2.24/2.46 tff(6726,plain,
% 2.24/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.46 inference(transitivity,[status(thm)],[6725, 6723])).
% 2.24/2.46 tff(6727,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)))),
% 2.24/2.46 inference(quant_inst,[status(thm)],[])).
% 2.24/2.46 tff(6728,plain,
% 2.24/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6727, 6726])).
% 2.24/2.46 tff(6729,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6728, 106, 1446, 769, 2027, 126])).
% 2.24/2.46 tff(6730,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6731,plain,
% 2.24/2.46 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[6730, 6722, 1446, 126])).
% 2.24/2.46 tff(6732,plain,
% 2.24/2.46 (s(s(s(s(s(z))))) = elem!1),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[853, 6731, 5041])).
% 2.24/2.46 tff(6733,plain,
% 2.24/2.46 (elem!1 = s(s(s(s(s(z)))))),
% 2.24/2.46 inference(modus_ponens,[status(thm)],[6732, 759])).
% 2.24/2.46 tff(6734,plain,
% 2.24/2.46 ($false),
% 2.24/2.46 inference(unit_resolution,[status(thm)],[1908, 6733])).
% 2.24/2.46 tff(6735,plain,((elem!1 = s(s(s(s(s(z)))))) | b(s(s(s(s(s(z))))), elem!1) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.46 tff(6736,plain,
% 2.24/2.46 (b(s(s(s(s(s(z))))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6735, 6720, 1446, 126, 1908])).
% 2.24/2.47 tff(6737,plain,
% 2.24/2.47 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[365, 357, 259, 323])).
% 2.24/2.47 tff(6738,plain,
% 2.24/2.47 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[374, 6737, 355])).
% 2.24/2.47 tff(6739,plain,
% 2.24/2.47 (~b(z, s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5201, 207, 259, 323, 159])).
% 2.24/2.47 tff(6740,plain,
% 2.24/2.47 (r(z, s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[124, 6739])).
% 2.24/2.47 tff(6741,plain,
% 2.24/2.47 (~r(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6247, 6740, 637, 6738])).
% 2.24/2.47 tff(6742,plain,
% 2.24/2.47 (b(z, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[293, 6741])).
% 2.24/2.47 tff(6743,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6744,plain,
% 2.24/2.47 (((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6745,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6744])).
% 2.24/2.47 tff(6746,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6745, 6743])).
% 2.24/2.47 tff(6747,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6748,plain,
% 2.24/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6747, 6746])).
% 2.24/2.47 tff(6749,plain,
% 2.24/2.47 ((~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), elem!1))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6748, 171, 6706, 159, 357, 6742])).
% 2.24/2.47 tff(6750,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6749, 6736, 6710])).
% 2.24/2.47 tff(6751,plain,(r(elem!1, s(z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | (~b(s(z), s(s(z)))) | (elem!1 = s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6752,plain,
% 2.24/2.47 (r(elem!1, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6751, 1908, 6705, 1446, 126, 4903, 4905, 207, 5541, 637, 2116, 733, 6504, 1437, 84])).
% 2.24/2.47 tff(6753,plain,
% 2.24/2.47 (~(elem!1 = z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1351, 6752, 94, 4905, 95, 733])).
% 2.24/2.47 tff(6754,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6564, 6753, 6752, 207, 5541, 160, 1908, 95, 6703, 502])).
% 2.24/2.47 tff(6755,plain,((elem!1 = 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))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | b(s(s(z)), elem!1) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (s(s(z)) = elem!1) | (elem!1 = s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6756,plain,
% 2.24/2.47 (elem!1 = s(s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6755, 6701, 160, 95, 5277, 6529, 1446, 126, 637, 2116, 1437, 84])).
% 2.24/2.47 tff(6757,plain,
% 2.24/2.47 (s(s(s(s(s(z))))) = elem!1),
% 2.24/2.47 inference(symmetry,[status(thm)],[6756])).
% 2.24/2.47 tff(6758,plain,
% 2.24/2.47 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6757])).
% 2.24/2.47 tff(6759,plain,
% 2.24/2.47 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.24/2.47 inference(transitivity,[status(thm)],[6758, 3511])).
% 2.24/2.47 tff(6760,plain,
% 2.24/2.47 ((s(s(s(elem!1))) = elem!1) <=> (s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6759])).
% 2.24/2.47 tff(6761,plain,
% 2.24/2.47 (~r(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3442, 6756, 4902])).
% 2.24/2.47 tff(6762,plain,
% 2.24/2.47 (~b(elem!1, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5251, 6756, 5247])).
% 2.24/2.47 tff(6763,plain,
% 2.24/2.47 (r(elem!1, s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[687, 6762, 1437])).
% 2.24/2.47 tff(6764,plain,
% 2.24/2.47 (~(elem!1 = z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1351, 6763, 94, 4905, 95, 6701])).
% 2.24/2.47 tff(6765,plain,
% 2.24/2.47 (b(elem!1, z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1567, 6764, 6761])).
% 2.24/2.47 tff(6766,plain,
% 2.24/2.47 (b(z, elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1382, 6763, 94, 4905, 95, 6701])).
% 2.24/2.47 tff(6767,plain,
% 2.24/2.47 (r(s(s(z)), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1416, 6701, 2116])).
% 2.24/2.47 tff(6768,plain,
% 2.24/2.47 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5129, 6765, 94, 637, 3829, 6650, 4905, 6767, 6766, 95, 6763])).
% 2.24/2.47 tff(6769,plain,
% 2.24/2.47 (b(s(s(s(elem!1))), s(s(z)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1013, 6768])).
% 2.24/2.47 tff(6770,plain,
% 2.24/2.47 (s(s(s(elem!1))) = elem!1),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[5056, 6769, 6763, 6766, 6765, 6504, 4905, 94, 95])).
% 2.24/2.47 tff(6771,plain,
% 2.24/2.47 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6770, 6760])).
% 2.24/2.47 tff(6772,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3829, 6771])).
% 2.24/2.47 tff(6773,plain,((s(s(z)) = elem!1) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (elem!1 = s(z)) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | b(z, s(z)) | r(s(s(s(s(s(z))))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6774,plain,
% 2.24/2.47 (s(s(z)) = elem!1),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6773, 1437, 637, 95, 5247, 160, 6642, 61, 84, 219])).
% 2.24/2.47 tff(6775,plain,
% 2.24/2.47 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6774])).
% 2.24/2.47 tff(6776,plain,
% 2.24/2.47 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6775])).
% 2.24/2.47 tff(6777,plain,
% 2.24/2.47 (r(s(z), s(s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6642, 6776])).
% 2.24/2.47 tff(6778,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6503, 6777])).
% 2.24/2.47 tff(6779,plain,((elem!1 = s(z)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | b(s(s(s(s(s(z))))), s(z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | b(z, s(z)) | r(s(s(s(s(s(z))))), s(s(z))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6780,plain,
% 2.24/2.47 (elem!1 = s(z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6779, 5247, 95, 637, 6528, 84, 6520, 32])).
% 2.24/2.47 tff(6781,plain,
% 2.24/2.47 (s(z) = elem!1),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[1428, 2154])).
% 2.24/2.47 tff(6782,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1651, 6781])).
% 2.24/2.47 tff(6783,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6784,plain,
% 2.24/2.47 (s(z) = elem!1),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6783, 6780])).
% 2.24/2.47 tff(6785,plain,
% 2.24/2.47 (~b(z, elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4918, 6784, 84])).
% 2.24/2.47 tff(6786,plain,
% 2.24/2.47 (r(s(z), elem!1) <=> r(s(z), s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[1428])).
% 2.24/2.47 tff(6787,plain,
% 2.24/2.47 (r(s(z), s(z)) <=> r(s(z), elem!1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[6786])).
% 2.24/2.47 tff(6788,plain,
% 2.24/2.47 ((~r(s(z), s(z))) <=> (~r(s(z), elem!1))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6787])).
% 2.24/2.47 tff(6789,plain,
% 2.24/2.47 ((~![X: $i] : (~r(X, X))) | (~r(s(z), s(z)))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6790,plain,
% 2.24/2.47 (~r(s(z), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6789, 3994])).
% 2.24/2.47 tff(6791,plain,
% 2.24/2.47 (~r(s(z), elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6790, 6788])).
% 2.24/2.47 tff(6792,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1446, 6791])).
% 2.24/2.47 tff(6793,plain,((~(elem!1 = s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6794,plain,
% 2.24/2.47 (~r(s(z), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6793, 6780])).
% 2.24/2.47 tff(6795,plain,
% 2.24/2.47 (~(z = elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1927, 6794, 95])).
% 2.24/2.47 tff(6796,plain,
% 2.24/2.47 (r(z, elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[651, 6795, 6785])).
% 2.24/2.47 tff(6797,plain,
% 2.24/2.47 (~b(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2702, 6796, 6506, 637, 6510, 95])).
% 2.24/2.47 tff(6798,plain,
% 2.24/2.47 (r(s(s(s(z))), s(z))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1173, 6797])).
% 2.24/2.47 tff(6799,plain,
% 2.24/2.47 (~r(s(s(s(z))), z)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[794, 106, 94, 95, 6798])).
% 2.24/2.47 tff(6800,plain,
% 2.24/2.47 (r(s(s(s(z))), s(z)) <=> r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(monotonicity,[status(thm)],[1435])).
% 2.24/2.47 tff(6801,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(z))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6800])).
% 2.24/2.47 tff(6802,plain,
% 2.24/2.47 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6801])).
% 2.24/2.47 tff(6803,plain,
% 2.24/2.47 (~r(s(s(s(z))), s(z))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[799, 6802])).
% 2.24/2.47 tff(6804,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[747, 6803])).
% 2.24/2.47 tff(6805,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(z))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6806,plain,
% 2.24/2.47 (r(s(s(s(z))), elem!1)),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6805, 6798, 6784])).
% 2.24/2.47 tff(6807,plain,
% 2.24/2.47 (s(elem!1) = s(s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6780])).
% 2.24/2.47 tff(6808,plain,
% 2.24/2.47 (s(s(elem!1)) = s(s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6807])).
% 2.24/2.47 tff(6809,plain,
% 2.24/2.47 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6780, 6808])).
% 2.24/2.47 tff(6810,plain,
% 2.24/2.47 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6809, 4075])).
% 2.24/2.47 tff(6811,plain,
% 2.24/2.47 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6810])).
% 2.24/2.47 tff(6812,plain,
% 2.24/2.47 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6811])).
% 2.24/2.47 tff(6813,plain,
% 2.24/2.47 (~(elem!1 = s(s(elem!1)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[344, 6812])).
% 2.24/2.47 tff(6814,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6815,plain,
% 2.24/2.47 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6816,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6815])).
% 2.24/2.47 tff(6817,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6816, 6814])).
% 2.24/2.47 tff(6818,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6819,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6818, 6817])).
% 2.24/2.47 tff(6820,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6819, 106, 5609, 502, 3, 569])).
% 2.24/2.47 tff(6821,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6822,plain,
% 2.24/2.47 (~r(s(z), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6821, 6516, 5609, 5277])).
% 2.24/2.47 tff(6823,plain,
% 2.24/2.47 (b(s(z), s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[454, 6822, 254])).
% 2.24/2.47 tff(6824,plain,
% 2.24/2.47 (b(elem!1, s(s(s(s(z)))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4096, 6780, 6823])).
% 2.24/2.47 tff(6825,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6780])).
% 2.24/2.47 tff(6826,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(symmetry,[status(thm)],[6825])).
% 2.24/2.47 tff(6827,plain,
% 2.24/2.47 (b(s(s(s(s(z)))), elem!1)),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6510, 6826])).
% 2.24/2.47 tff(6828,plain,
% 2.24/2.47 (b(elem!1, s(s(z))) <=> b(s(z), s(s(z)))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6780])).
% 2.24/2.47 tff(6829,plain,
% 2.24/2.47 (b(s(z), s(s(z))) <=> b(elem!1, s(s(z)))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6828])).
% 2.24/2.47 tff(6830,plain,
% 2.24/2.47 (b(elem!1, s(s(z)))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6504, 6829])).
% 2.24/2.47 tff(6831,plain,
% 2.24/2.47 (~b(elem!1, s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4195, 6830, 6514, 6780, 6516, 6827, 6824])).
% 2.24/2.47 tff(6832,plain,
% 2.24/2.47 (r(elem!1, s(s(elem!1)))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4200, 6831, 6813])).
% 2.24/2.47 tff(6833,plain,
% 2.24/2.47 (r(s(z), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4206, 6832, 6780])).
% 2.24/2.47 tff(6834,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6835,plain,
% 2.24/2.47 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6836,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6835])).
% 2.24/2.47 tff(6837,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6836, 6834])).
% 2.24/2.47 tff(6838,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6839,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6838, 6837])).
% 2.24/2.47 tff(6840,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6839, 106, 2049, 126, 1357, 1998])).
% 2.24/2.47 tff(6841,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6842,plain,
% 2.24/2.47 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6841, 6833, 61, 6806])).
% 2.24/2.47 tff(6843,plain,
% 2.24/2.47 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[1368, 6842])).
% 2.24/2.47 tff(6844,plain,
% 2.24/2.47 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[4847, 6780, 32])).
% 2.24/2.47 tff(6845,plain,
% 2.24/2.47 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[3251, 6796, 6507])).
% 2.24/2.47 tff(6846,plain,
% 2.24/2.47 (r(elem!1, s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[782, 6845, 6844])).
% 2.24/2.47 tff(6847,plain,
% 2.24/2.47 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(s(z))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6780])).
% 2.24/2.47 tff(6848,plain,
% 2.24/2.47 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.24/2.47 inference(symmetry,[status(thm)],[6847])).
% 2.24/2.47 tff(6849,plain,
% 2.24/2.47 (r(elem!1, s(s(s(z))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6833, 6848])).
% 2.24/2.47 tff(6850,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6851,plain,
% 2.24/2.47 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6852,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.24/2.47 inference(monotonicity,[status(thm)],[6851])).
% 2.24/2.47 tff(6853,plain,
% 2.24/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.24/2.47 inference(transitivity,[status(thm)],[6852, 6850])).
% 2.24/2.47 tff(6854,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 2.24/2.47 inference(quant_inst,[status(thm)],[])).
% 2.24/2.47 tff(6855,plain,
% 2.24/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.24/2.47 inference(modus_ponens,[status(thm)],[6854, 6853])).
% 2.24/2.47 tff(6856,plain,
% 2.24/2.47 ($false),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6855, 106, 1426, 769, 2604, 502])).
% 2.24/2.47 tff(6857,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.47 tff(6858,plain,
% 2.24/2.47 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[6857, 6849, 5277, 6846])).
% 2.24/2.47 tff(6859,plain,
% 2.24/2.47 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.24/2.47 inference(unit_resolution,[status(thm)],[2614, 6858])).
% 2.24/2.47 tff(6860,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6861,plain,
% 2.24/2.47 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.24/2.47 inference(rewrite,[status(thm)],[])).
% 2.24/2.47 tff(6862,plain,
% 2.24/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6861])).
% 2.24/2.48 tff(6863,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6862, 6860])).
% 2.24/2.48 tff(6864,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6865,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6864, 6863])).
% 2.24/2.48 tff(6866,plain,
% 2.24/2.48 (~b(s(s(s(z))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6865, 171, 6859, 6843, 6508])).
% 2.24/2.48 tff(6867,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[953, 25, 194, 6866, 6799])).
% 2.24/2.48 tff(6868,plain,(b(s(s(s(s(s(z))))), s(z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | b(z, s(z)) | b(s(z), s(s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6869,plain,
% 2.24/2.48 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6868, 637, 95, 84, 32, 5609])).
% 2.24/2.48 tff(6870,plain,
% 2.24/2.48 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[471, 171, 6504, 6506, 6869])).
% 2.24/2.48 tff(6871,plain,
% 2.24/2.48 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[225, 6870])).
% 2.24/2.48 tff(6872,plain,
% 2.24/2.48 (~r(z, s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6331, 6871, 61, 95])).
% 2.24/2.48 tff(6873,plain,
% 2.24/2.48 (b(z, s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[498, 6872])).
% 2.24/2.48 tff(6874,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5213, 106, 96, 95, 263, 2118])).
% 2.24/2.48 tff(6875,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6876,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6875, 263, 95, 96])).
% 2.24/2.48 tff(6877,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[274, 6876])).
% 2.24/2.48 tff(6878,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6879,plain,
% 2.24/2.48 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6880,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6879])).
% 2.24/2.48 tff(6881,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6880, 6878])).
% 2.24/2.48 tff(6882,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6883,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6882, 6881])).
% 2.24/2.48 tff(6884,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6883, 106, 260, 5609, 126, 263])).
% 2.24/2.48 tff(6885,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6886,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6885, 263, 126, 5609])).
% 2.24/2.48 tff(6887,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3668, 6886])).
% 2.24/2.48 tff(6888,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6889,plain,
% 2.24/2.48 (((~b(s(s(s(s(s(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))))), 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(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6890,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6889])).
% 2.24/2.48 tff(6891,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6890, 6888])).
% 2.24/2.48 tff(6892,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6893,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6892, 6891])).
% 2.24/2.48 tff(6894,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6893, 171, 6887, 4, 146, 1313, 6877])).
% 2.24/2.48 tff(6895,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6896,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6895, 6869, 6873, 95, 94, 61, 5609])).
% 2.24/2.48 tff(6897,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[321, 6896, 255])).
% 2.24/2.48 tff(6898,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[365, 6897, 6506, 6504])).
% 2.24/2.48 tff(6899,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[374, 6898, 355])).
% 2.24/2.48 tff(6900,plain,
% 2.24/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6901,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6902,plain,
% 2.24/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6901, 6900])).
% 2.24/2.48 tff(6903,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6902, 106, 96, 637, 569, 2118])).
% 2.24/2.48 tff(6904,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6905,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6904, 637, 94, 6899])).
% 2.24/2.48 tff(6906,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[274, 6905])).
% 2.24/2.48 tff(6907,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[473, 6897, 6506, 61, 6504, 6869])).
% 2.24/2.48 tff(6908,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3668, 6907])).
% 2.24/2.48 tff(6909,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6893, 171, 6908, 6869, 6502, 6873, 6906])).
% 2.24/2.48 tff(6910,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(z, s(z)) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6911,plain,
% 2.24/2.48 (~r(s(s(z)), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6910, 84, 5609, 95, 32])).
% 2.24/2.48 tff(6912,plain,
% 2.24/2.48 (b(s(s(z)), z)),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[157, 6911])).
% 2.24/2.48 tff(6913,plain,
% 2.24/2.48 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6914,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6913])).
% 2.24/2.48 tff(6915,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6914, 3695])).
% 2.24/2.48 tff(6916,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6917,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6916, 6915])).
% 2.24/2.48 tff(6918,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6917, 171, 1, 146, 6333])).
% 2.24/2.48 tff(6919,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[205, 6918])).
% 2.24/2.48 tff(6920,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[3978, 502, 95, 96, 6333])).
% 2.24/2.48 tff(6921,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[321, 6920, 255])).
% 2.24/2.48 tff(6922,plain,
% 2.24/2.48 (~r(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6169, 6919, 126, 502])).
% 2.24/2.48 tff(6923,plain,
% 2.24/2.48 (b(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[550, 6922])).
% 2.24/2.48 tff(6924,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[365, 6923, 5174, 6921])).
% 2.24/2.48 tff(6925,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[374, 6924, 355])).
% 2.24/2.48 tff(6926,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[434, 106, 5609, 396, 6925, 6919])).
% 2.24/2.48 tff(6927,plain,((~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(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6928,plain,
% 2.24/2.48 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6927, 396, 5609, 126, 1, 95, 96])).
% 2.24/2.48 tff(6929,plain,
% 2.24/2.48 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[479, 6928])).
% 2.24/2.48 tff(6930,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6931,plain,
% 2.24/2.48 (((~b(s(s(s(s(s(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))))), z)) | (~b(s(s(z)), 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)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6932,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6931])).
% 2.24/2.48 tff(6933,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6932, 6930])).
% 2.24/2.48 tff(6934,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6935,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6934, 6933])).
% 2.24/2.48 tff(6936,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6935, 171, 1, 4, 160, 159, 1313])).
% 2.24/2.48 tff(6937,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6938,plain,
% 2.24/2.48 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6937, 6929, 1, 146, 6333])).
% 2.24/2.48 tff(6939,plain,
% 2.24/2.48 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[205, 6938])).
% 2.24/2.48 tff(6940,plain,
% 2.24/2.48 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6895, 6929, 6333, 95, 96, 126, 5609])).
% 2.24/2.48 tff(6941,plain,
% 2.24/2.48 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[321, 6940, 255])).
% 2.24/2.48 tff(6942,plain,
% 2.24/2.48 (~b(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[5197, 501, 126, 96, 554, 95])).
% 2.24/2.48 tff(6943,plain,
% 2.24/2.48 (~r(z, s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[624, 501, 96, 554])).
% 2.24/2.48 tff(6944,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[124, 6943, 6942])).
% 2.24/2.48 tff(6945,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6946,plain,
% 2.24/2.48 (~r(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6945, 6939, 96, 126, 95])).
% 2.24/2.48 tff(6947,plain,
% 2.24/2.48 (b(s(z), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[550, 6946])).
% 2.24/2.48 tff(6948,plain,
% 2.24/2.48 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[365, 6947, 5174, 6941])).
% 2.24/2.48 tff(6949,plain,
% 2.24/2.48 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[374, 6948, 355])).
% 2.24/2.48 tff(6950,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[434, 106, 5609, 396, 6949, 6939])).
% 2.24/2.48 tff(6951,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.48 tff(6952,plain,
% 2.24/2.48 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6951, 94, 5609, 61, 95, 6912])).
% 2.24/2.48 tff(6953,plain,
% 2.24/2.48 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[225, 6952])).
% 2.24/2.48 tff(6954,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6955,plain,
% 2.24/2.48 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(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(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(rewrite,[status(thm)],[])).
% 2.24/2.48 tff(6956,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.24/2.48 inference(monotonicity,[status(thm)],[6955])).
% 2.24/2.48 tff(6957,plain,
% 2.24/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.24/2.48 inference(transitivity,[status(thm)],[6956, 6954])).
% 2.24/2.48 tff(6958,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(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)))))),
% 2.24/2.48 inference(quant_inst,[status(thm)],[])).
% 2.24/2.48 tff(6959,plain,
% 2.24/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.24/2.48 inference(modus_ponens,[status(thm)],[6958, 6957])).
% 2.24/2.48 tff(6960,plain,
% 2.24/2.48 ($false),
% 2.24/2.48 inference(unit_resolution,[status(thm)],[6959, 171, 1, 207, 159, 1313])).
% 2.24/2.49 tff(6961,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(6962,plain,
% 2.24/2.49 (~b(z, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6961, 6912, 6953, 6502])).
% 2.24/2.49 tff(6963,plain,
% 2.24/2.49 (r(z, s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[498, 6962])).
% 2.24/2.49 tff(6964,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(6965,plain,
% 2.24/2.49 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(6966,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6965])).
% 2.24/2.49 tff(6967,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[6966, 6964])).
% 2.24/2.49 tff(6968,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(6969,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[6968, 6967])).
% 2.24/2.49 tff(6970,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6969, 106, 94, 5609, 61, 6963])).
% 2.24/2.49 tff(6971,plain,(b(z, s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(6972,plain,
% 2.24/2.49 (b(z, s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6971, 5609, 95, 32])).
% 2.24/2.49 tff(6973,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(6974,plain,
% 2.24/2.49 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(6975,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6974])).
% 2.24/2.49 tff(6976,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[6975, 6973])).
% 2.24/2.49 tff(6977,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(6978,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[6977, 6976])).
% 2.24/2.49 tff(6979,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6978, 106, 95, 600, 126, 127])).
% 2.24/2.49 tff(6980,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(6981,plain,
% 2.24/2.49 (~r(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6980, 127, 126, 95])).
% 2.24/2.49 tff(6982,plain,
% 2.24/2.49 (b(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[124, 6981])).
% 2.24/2.49 tff(6983,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5633, 106, 2, 5609, 126, 501])).
% 2.24/2.49 tff(6984,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(6985,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6984, 2, 5609, 126])).
% 2.24/2.49 tff(6986,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[205, 6985])).
% 2.24/2.49 tff(6987,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5797, 5908, 2, 160, 5598, 355])).
% 2.24/2.49 tff(6988,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3668, 6987])).
% 2.24/2.49 tff(6989,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5678, 6988, 127, 126])).
% 2.24/2.49 tff(6990,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[479, 6989])).
% 2.24/2.49 tff(6991,plain,
% 2.24/2.49 (((~b(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))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(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(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(6992,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[6991])).
% 2.24/2.49 tff(6993,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[6992, 5785])).
% 2.24/2.49 tff(6994,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(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))))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(6995,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[6994, 6993])).
% 2.24/2.49 tff(6996,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6995, 171, 161, 5835, 5827, 1313])).
% 2.24/2.49 tff(6997,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(6998,plain,
% 2.24/2.49 (~b(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6997, 6990, 5598, 2, 95, 126])).
% 2.24/2.49 tff(6999,plain,
% 2.24/2.49 (r(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[124, 6998])).
% 2.24/2.49 tff(7000,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5916, 106, 554, 2, 95, 6999])).
% 2.24/2.49 tff(7001,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7002,plain,
% 2.24/2.49 (~r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7001, 2, 95, 126, 127, 6986])).
% 2.24/2.49 tff(7003,plain,
% 2.24/2.49 (b(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[550, 7002])).
% 2.24/2.49 tff(7004,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5678, 260, 127, 126])).
% 2.24/2.49 tff(7005,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[479, 7004])).
% 2.24/2.49 tff(7006,plain,
% 2.24/2.49 (~b(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6997, 7005, 5598, 2, 95, 126])).
% 2.24/2.49 tff(7007,plain,
% 2.24/2.49 (r(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[124, 7006])).
% 2.24/2.49 tff(7008,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5851, 7005, 95, 2, 323, 5604])).
% 2.24/2.49 tff(7009,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[374, 7008, 355])).
% 2.24/2.49 tff(7010,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6123, 7009, 7007, 95, 2, 3281, 323])).
% 2.24/2.49 tff(7011,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7012,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7011, 2, 95, 3281, 7003, 126, 127])).
% 2.24/2.49 tff(7013,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[3668, 7012])).
% 2.24/2.49 tff(7014,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z, s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7015,plain,
% 2.24/2.49 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7016,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z, s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7015])).
% 2.24/2.49 tff(7017,plain,
% 2.24/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z, s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7016, 7014])).
% 2.24/2.49 tff(7018,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7019,plain,
% 2.24/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z, s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7018, 7017])).
% 2.24/2.49 tff(7020,plain,
% 2.24/2.49 (~b(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7019, 171, 7003, 3281, 7013, 6986, 5589])).
% 2.24/2.49 tff(7021,plain,
% 2.24/2.49 (r(s(s(s(s(z)))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[321, 7020, 255])).
% 2.24/2.49 tff(7022,plain,
% 2.24/2.49 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6149, 7021, 95, 2])).
% 2.24/2.49 tff(7023,plain,
% 2.24/2.49 (b(s(s(s(s(z)))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[374, 7022, 355])).
% 2.24/2.49 tff(7024,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7025,plain,
% 2.24/2.49 (((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7026,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.24/2.49 inference(monotonicity,[status(thm)],[7025])).
% 2.24/2.49 tff(7027,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(transitivity,[status(thm)],[7026, 7024])).
% 2.24/2.49 tff(7028,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.24/2.49 inference(quant_inst,[status(thm)],[])).
% 2.24/2.49 tff(7029,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.24/2.49 inference(modus_ponens,[status(thm)],[7028, 7027])).
% 2.24/2.49 tff(7030,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7029, 106, 2, 95, 7021])).
% 2.24/2.49 tff(7031,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(z)))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[351, 7030])).
% 2.24/2.49 tff(7032,plain,
% 2.24/2.49 (~b(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5981, 7031, 7023, 5589])).
% 2.24/2.49 tff(7033,plain,
% 2.24/2.49 (r(z, s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[124, 7032])).
% 2.24/2.49 tff(7034,plain,
% 2.24/2.49 (~r(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6001, 7033, 95, 2])).
% 2.24/2.49 tff(7035,plain,
% 2.24/2.49 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5797, 7013, 2, 6986, 5598, 355])).
% 2.24/2.49 tff(7036,plain,
% 2.24/2.49 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[225, 7035])).
% 2.24/2.49 tff(7037,plain,
% 2.24/2.49 (~r(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[5694, 7036, 126, 2])).
% 2.24/2.49 tff(7038,plain,
% 2.24/2.49 (b(s(s(s(s(s(z))))), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[479, 7037])).
% 2.24/2.49 tff(7039,plain,
% 2.24/2.49 (~b(s(s(z)), z)),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6046, 7033, 3281, 7003, 7036, 2, 7038])).
% 2.24/2.49 tff(7040,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[157, 7039, 7034])).
% 2.24/2.49 tff(7041,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), 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(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7042,plain,
% 2.24/2.49 (~r(s(s(z)), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7041, 127, 95, 126, 3281, 5609])).
% 2.24/2.49 tff(7043,plain,
% 2.24/2.49 (b(s(s(z)), s(z))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[244, 7042])).
% 2.24/2.49 tff(7044,plain,
% 2.24/2.49 ($false),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6227, 171, 323, 3281, 259, 161])).
% 2.24/2.49 tff(7045,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.49 tff(7046,plain,
% 2.24/2.49 (~b(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[7045, 7043, 3281, 6982])).
% 2.24/2.49 tff(7047,plain,
% 2.24/2.49 (r(s(z), s(s(z)))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[550, 7046])).
% 2.24/2.49 tff(7048,plain,
% 2.24/2.49 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[6169, 502, 126, 554])).
% 2.24/2.49 tff(7049,plain,
% 2.24/2.49 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.24/2.49 inference(unit_resolution,[status(thm)],[205, 7048])).
% 2.24/2.49 tff(7050,plain,
% 2.24/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.49 inference(rewrite,[status(thm)],[])).
% 2.24/2.49 tff(7051,plain,
% 2.24/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(7052,plain,
% 2.24/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[7051, 7050])).
% 2.24/2.50 tff(7053,plain,
% 2.24/2.50 ($false),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7052, 106, 554, 5609, 502, 263])).
% 2.24/2.50 tff(7054,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.24/2.50 tff(7055,plain,
% 2.24/2.50 (~r(s(s(s(s(z)))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[7054, 502, 5609, 554])).
% 2.24/2.50 tff(7056,plain,
% 2.24/2.50 (b(s(s(s(s(z)))), s(z))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[321, 7055, 255])).
% 2.24/2.50 tff(7057,plain,
% 2.24/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[566, 356, 259, 357])).
% 2.24/2.50 tff(7058,plain,
% 2.24/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[454, 7057, 254])).
% 2.24/2.50 tff(7059,plain,
% 2.24/2.50 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[5760, 356, 160, 207])).
% 2.24/2.50 tff(7060,plain,
% 2.24/2.50 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.24/2.50 inference(unit_resolution,[status(thm)],[3668, 7059])).
% 2.24/2.50 tff(7061,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(7062,plain,
% 2.24/2.50 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.50 inference(rewrite,[status(thm)],[])).
% 2.24/2.50 tff(7063,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.24/2.50 inference(monotonicity,[status(thm)],[7062])).
% 2.24/2.50 tff(7064,plain,
% 2.24/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.50 inference(transitivity,[status(thm)],[7063, 7061])).
% 2.24/2.50 tff(7065,plain,
% 2.24/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.24/2.50 inference(quant_inst,[status(thm)],[])).
% 2.24/2.50 tff(7066,plain,
% 2.24/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.24/2.50 inference(modus_ponens,[status(thm)],[7065, 7064])).
% 2.34/2.50 tff(7067,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7066, 106, 260, 5609, 502, 3])).
% 2.34/2.50 tff(7068,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7069,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7068, 7060, 7058, 5609, 502])).
% 2.34/2.50 tff(7070,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7071,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7070, 207, 502, 160, 5609, 259, 7056])).
% 2.34/2.50 tff(7072,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[374, 7071, 355])).
% 2.34/2.50 tff(7073,plain,
% 2.34/2.50 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6821, 7072, 5609, 502])).
% 2.34/2.50 tff(7074,plain,
% 2.34/2.50 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[454, 7073, 254])).
% 2.34/2.50 tff(7075,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(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(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(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(s(s(z))))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7076,plain,
% 2.34/2.50 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(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(s(s(z))))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7077,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(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(s(s(z)))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7076])).
% 2.34/2.50 tff(7078,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(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(s(s(z))))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7077, 7075])).
% 2.34/2.50 tff(7079,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), 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)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7080,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7079, 7078])).
% 2.34/2.50 tff(7081,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7080, 171, 3281, 259, 1, 160, 207, 1313])).
% 2.34/2.50 tff(7082,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7083,plain,
% 2.34/2.50 (~b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7082, 207, 3281, 1313, 259, 160])).
% 2.34/2.50 tff(7084,plain,
% 2.34/2.50 (r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[157, 7083])).
% 2.34/2.50 tff(7085,plain,
% 2.34/2.50 (~r(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2952, 7084, 554, 95])).
% 2.34/2.50 tff(7086,plain,
% 2.34/2.50 (b(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[124, 7085])).
% 2.34/2.50 tff(7087,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6201, 171, 3281, 259, 7086, 7074, 7056])).
% 2.34/2.50 tff(7088,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z))) | (~b(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))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7089,plain,
% 2.34/2.50 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7088, 502, 259, 5609, 3281, 7049, 554, 95, 1313])).
% 2.34/2.50 tff(7090,plain,
% 2.34/2.50 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[225, 7089])).
% 2.34/2.50 tff(7091,plain,
% 2.34/2.50 (~r(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[3167, 7090, 126, 554])).
% 2.34/2.50 tff(7092,plain,
% 2.34/2.50 (b(s(s(z)), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[157, 7091])).
% 2.34/2.50 tff(7093,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7094,plain,
% 2.34/2.50 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7095,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7094])).
% 2.34/2.50 tff(7096,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7095, 7093])).
% 2.34/2.50 tff(7097,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7098,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7097, 7096])).
% 2.34/2.50 tff(7099,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7098, 171, 3281, 259, 1, 376, 357])).
% 2.34/2.50 tff(7100,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7101,plain,
% 2.34/2.50 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7100, 7092, 259, 3281, 7056])).
% 2.34/2.50 tff(7102,plain,
% 2.34/2.50 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[454, 7101, 254])).
% 2.34/2.50 tff(7103,plain,
% 2.34/2.50 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[6821, 7102, 5609, 502])).
% 2.34/2.50 tff(7104,plain,
% 2.34/2.50 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[374, 7103, 355])).
% 2.34/2.50 tff(7105,plain,
% 2.34/2.50 (~b(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[2535, 7104, 2527, 7092])).
% 2.34/2.50 tff(7106,plain,
% 2.34/2.50 (r(s(s(s(s(z)))), z)),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[274, 7105])).
% 2.34/2.50 tff(7107,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7108,plain,
% 2.34/2.50 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7109,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7108])).
% 2.34/2.50 tff(7110,plain,
% 2.34/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7109, 7107])).
% 2.34/2.50 tff(7111,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7112,plain,
% 2.34/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7111, 7110])).
% 2.34/2.50 tff(7113,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7112, 171, 3281, 161, 1, 357, 356, 2527])).
% 2.34/2.50 tff(7114,plain,((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7115,plain,
% 2.34/2.50 (~b(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7114, 7092, 3281, 7056, 7104, 2527])).
% 2.34/2.50 tff(7116,plain,
% 2.34/2.50 (r(z, s(s(z)))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[124, 7115])).
% 2.34/2.50 tff(7117,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7118,plain,
% 2.34/2.50 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(rewrite,[status(thm)],[])).
% 2.34/2.50 tff(7119,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.34/2.50 inference(monotonicity,[status(thm)],[7118])).
% 2.34/2.50 tff(7120,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.34/2.50 inference(transitivity,[status(thm)],[7119, 7117])).
% 2.34/2.50 tff(7121,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.34/2.50 inference(quant_inst,[status(thm)],[])).
% 2.34/2.50 tff(7122,plain,
% 2.34/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.34/2.50 inference(modus_ponens,[status(thm)],[7121, 7120])).
% 2.34/2.50 tff(7123,plain,
% 2.34/2.50 ($false),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7122, 106, 95, 7116, 7102, 7106])).
% 2.34/2.50 tff(7124,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.50 tff(7125,plain,
% 2.34/2.50 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[7124, 7047, 3281, 5589, 5609, 7043, 126, 95, 5598])).
% 2.34/2.50 tff(7126,plain,
% 2.34/2.50 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.50 inference(unit_resolution,[status(thm)],[479, 7125])).
% 2.34/2.50 tff(7127,plain,
% 2.34/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7128,plain,
% 2.34/2.51 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(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(z), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7129,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7128])).
% 2.34/2.51 tff(7130,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7129, 7127])).
% 2.34/2.51 tff(7131,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7132,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7131, 7130])).
% 2.34/2.51 tff(7133,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7132, 106, 554, 5609, 126, 501])).
% 2.34/2.51 tff(7134,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7135,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7134, 7047, 5609, 126])).
% 2.34/2.51 tff(7136,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[205, 7135])).
% 2.34/2.51 tff(7137,plain,
% 2.34/2.51 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[225, 3447])).
% 2.34/2.51 tff(7138,plain,
% 2.34/2.51 (~r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2952, 637, 554, 95])).
% 2.34/2.51 tff(7139,plain,
% 2.34/2.51 (b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[124, 7138])).
% 2.34/2.51 tff(7140,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7141,plain,
% 2.34/2.51 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(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(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(z))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7142,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(z)))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7141])).
% 2.34/2.51 tff(7143,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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(z))))), s(z))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7142, 7140])).
% 2.34/2.51 tff(7144,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(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))))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7145,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7144, 7143])).
% 2.34/2.51 tff(7146,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7145, 171, 7139, 4, 160, 7137, 1313])).
% 2.34/2.51 tff(7147,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7148,plain,
% 2.34/2.51 (~r(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7147, 7136, 7126, 5598, 7047, 95, 126])).
% 2.34/2.51 tff(7149,plain,
% 2.34/2.51 (b(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[157, 7148])).
% 2.34/2.51 tff(7150,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[5678, 7126, 127, 126])).
% 2.34/2.51 tff(7151,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[3668, 7150])).
% 2.34/2.51 tff(7152,plain,
% 2.34/2.51 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7124, 554, 3281, 2527, 5609, 259, 126, 95, 1313])).
% 2.34/2.51 tff(7153,plain,
% 2.34/2.51 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[479, 7152])).
% 2.34/2.51 tff(7154,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7155,plain,
% 2.34/2.51 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7156,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7155])).
% 2.34/2.51 tff(7157,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7156, 7154])).
% 2.34/2.51 tff(7158,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(z)))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7159,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7158, 7157])).
% 2.34/2.51 tff(7160,plain,
% 2.34/2.51 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7159, 171, 259, 3686, 4, 2527])).
% 2.34/2.51 tff(7161,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7160, 7139])).
% 2.34/2.51 tff(7162,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[351, 7161])).
% 2.34/2.51 tff(7163,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7164,plain,
% 2.34/2.51 (((~r(s(s(s(s(z)))), 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(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7165,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7164])).
% 2.34/2.51 tff(7166,plain,
% 2.34/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7165, 7163])).
% 2.34/2.51 tff(7167,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7168,plain,
% 2.34/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7167, 7166])).
% 2.34/2.51 tff(7169,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7168, 106, 5609, 263, 501, 500])).
% 2.34/2.51 tff(7170,plain,((~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(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7171,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7170, 7162, 263, 5609])).
% 2.34/2.51 tff(7172,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[205, 7171])).
% 2.34/2.51 tff(7173,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7145, 171, 7139, 4, 7172, 7137, 1313])).
% 2.34/2.51 tff(7174,plain,((~r(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7175,plain,
% 2.34/2.51 (~r(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7174, 263, 1313, 7153, 5609, 259, 3686, 2527, 554, 95, 126])).
% 2.34/2.51 tff(7176,plain,
% 2.34/2.51 (b(s(s(z)), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[157, 7175])).
% 2.34/2.51 tff(7177,plain,
% 2.34/2.51 (~r(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[2126, 600, 95, 263])).
% 2.34/2.51 tff(7178,plain,
% 2.34/2.51 (b(s(s(s(s(z)))), z)),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[274, 7177])).
% 2.34/2.51 tff(7179,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[608, 600, 95, 554])).
% 2.34/2.51 tff(7180,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[351, 7179])).
% 2.34/2.51 tff(7181,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7182,plain,
% 2.34/2.51 (((~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(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(rewrite,[status(thm)],[])).
% 2.34/2.51 tff(7183,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.51 inference(monotonicity,[status(thm)],[7182])).
% 2.34/2.51 tff(7184,plain,
% 2.34/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.51 inference(transitivity,[status(thm)],[7183, 7181])).
% 2.34/2.51 tff(7185,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.34/2.51 inference(quant_inst,[status(thm)],[])).
% 2.34/2.51 tff(7186,plain,
% 2.34/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.51 inference(modus_ponens,[status(thm)],[7185, 7184])).
% 2.34/2.51 tff(7187,plain,
% 2.34/2.51 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7186, 171, 1, 3686, 2527])).
% 2.34/2.51 tff(7188,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7187, 7180, 7178])).
% 2.34/2.51 tff(7189,plain,((~r(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7190,plain,
% 2.34/2.51 (~r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7189, 7176, 3686, 2527, 95, 554, 263])).
% 2.34/2.51 tff(7191,plain,
% 2.34/2.51 (b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[124, 7190])).
% 2.34/2.51 tff(7192,plain,
% 2.34/2.51 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7159, 171, 259, 3686, 7153, 2527])).
% 2.34/2.51 tff(7193,plain,
% 2.34/2.51 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7192, 7191])).
% 2.34/2.51 tff(7194,plain,
% 2.34/2.51 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[351, 7193])).
% 2.34/2.51 tff(7195,plain,
% 2.34/2.51 (~r(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[6419, 501, 95, 554])).
% 2.34/2.51 tff(7196,plain,
% 2.34/2.51 (b(z, s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[124, 7195])).
% 2.34/2.51 tff(7197,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7170, 501, 263, 5609])).
% 2.34/2.51 tff(7198,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[351, 7197])).
% 2.34/2.51 tff(7199,plain,
% 2.34/2.51 ($false),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7160, 7198, 7196])).
% 2.34/2.51 tff(7200,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.51 tff(7201,plain,
% 2.34/2.51 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7200, 263, 3686, 7153, 2527, 259, 5609, 95, 554])).
% 2.34/2.51 tff(7202,plain,
% 2.34/2.51 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[205, 7201])).
% 2.34/2.51 tff(7203,plain,
% 2.34/2.51 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.51 inference(unit_resolution,[status(thm)],[7082, 7202, 3281, 1313, 259, 7176])).
% 2.34/2.51 tff(7204,plain,
% 2.34/2.51 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[225, 7203])).
% 2.34/2.52 tff(7205,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~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)))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7206,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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)))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7207,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7206, 7205])).
% 2.34/2.52 tff(7208,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7207, 106, 5609, 7204, 263, 7194])).
% 2.34/2.52 tff(7209,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7210,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7209, 7151, 7043, 5609, 5589, 95, 7047, 3281, 5598, 126])).
% 2.34/2.52 tff(7211,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[321, 7210, 255])).
% 2.34/2.52 tff(7212,plain,
% 2.34/2.52 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7082, 7149, 3281, 5598, 7043, 7136])).
% 2.34/2.52 tff(7213,plain,
% 2.34/2.52 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[225, 7212])).
% 2.34/2.52 tff(7214,plain,
% 2.34/2.52 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7160, 161])).
% 2.34/2.52 tff(7215,plain,
% 2.34/2.52 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[351, 7214])).
% 2.34/2.52 tff(7216,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7114, 161, 3281, 357, 1, 2527])).
% 2.34/2.52 tff(7217,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[374, 7216, 355])).
% 2.34/2.52 tff(7218,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~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)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7219,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~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)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7220,plain,
% 2.34/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7219, 7218])).
% 2.34/2.52 tff(7221,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7220, 106, 5609, 396, 7217, 7215])).
% 2.34/2.52 tff(7222,plain,((~b(z, 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)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7223,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7222, 7213, 7211, 5609, 7043, 6982, 7126, 5589, 3281, 7151, 7149])).
% 2.34/2.52 tff(7224,plain,((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7225,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7224, 5609, 3281, 95, 126])).
% 2.34/2.52 tff(7226,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[145, 7225])).
% 2.34/2.52 tff(7227,plain,
% 2.34/2.52 (~r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6001, 2, 95, 600])).
% 2.34/2.52 tff(7228,plain,
% 2.34/2.52 (~b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5878, 2, 159, 3281, 502, 323, 95, 126])).
% 2.34/2.52 tff(7229,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[157, 7228, 7227])).
% 2.34/2.52 tff(7230,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7231,plain,
% 2.34/2.52 (~r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7230, 502, 3281, 7226, 323, 95, 126, 600])).
% 2.34/2.52 tff(7232,plain,
% 2.34/2.52 (b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[244, 7231])).
% 2.34/2.52 tff(7233,plain,
% 2.34/2.52 (~b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6237, 7232, 3281, 323])).
% 2.34/2.52 tff(7234,plain,
% 2.34/2.52 (r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[157, 7233])).
% 2.34/2.52 tff(7235,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[2126, 263, 95, 600])).
% 2.34/2.52 tff(7236,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[274, 7235])).
% 2.34/2.52 tff(7237,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7238,plain,
% 2.34/2.52 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7239,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7238])).
% 2.34/2.52 tff(7240,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7239, 7237])).
% 2.34/2.52 tff(7241,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7242,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7241, 7240])).
% 2.34/2.52 tff(7243,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7242, 171, 3281, 6887, 7226, 1313, 7236])).
% 2.34/2.52 tff(7244,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7245,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7244, 5541, 3281, 95, 600, 126, 5609])).
% 2.34/2.52 tff(7246,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[321, 7245, 255])).
% 2.34/2.52 tff(7247,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7248,plain,
% 2.34/2.52 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(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(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7249,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7248])).
% 2.34/2.52 tff(7250,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7249, 7247])).
% 2.34/2.52 tff(7251,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7252,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7251, 7250])).
% 2.34/2.52 tff(7253,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7252, 171, 323, 3281, 259, 357, 2527])).
% 2.34/2.52 tff(7254,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7255,plain,
% 2.34/2.52 (~b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7254, 7246, 3281, 323, 7232])).
% 2.34/2.52 tff(7256,plain,
% 2.34/2.52 (r(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[293, 7255])).
% 2.34/2.52 tff(7257,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[365, 7246, 7232, 323])).
% 2.34/2.52 tff(7258,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[374, 7257, 355])).
% 2.34/2.52 tff(7259,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6247, 7258, 7256, 600, 7234])).
% 2.34/2.52 tff(7260,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7261,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7260, 600, 323, 3281, 95, 126, 5609])).
% 2.34/2.52 tff(7262,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[479, 7261])).
% 2.34/2.52 tff(7263,plain,
% 2.34/2.52 (~b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6281, 7262, 3281, 7226, 323])).
% 2.34/2.52 tff(7264,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[244, 7263])).
% 2.34/2.52 tff(7265,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6123, 7264, 95, 600, 3281, 323])).
% 2.34/2.52 tff(7266,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[374, 7265, 355])).
% 2.34/2.52 tff(7267,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6984, 7264, 5609, 126])).
% 2.34/2.52 tff(7268,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[205, 7267])).
% 2.34/2.52 tff(7269,plain,
% 2.34/2.52 (~r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6001, 7264, 95, 600])).
% 2.34/2.52 tff(7270,plain,
% 2.34/2.52 (b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[157, 7269])).
% 2.34/2.52 tff(7271,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6046, 7270, 3281, 323, 600, 7264, 7262])).
% 2.34/2.52 tff(7272,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[225, 7271])).
% 2.34/2.52 tff(7273,plain,
% 2.34/2.52 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[5760, 7272, 7268, 7266])).
% 2.34/2.52 tff(7274,plain,
% 2.34/2.52 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3668, 7273])).
% 2.34/2.52 tff(7275,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6885, 7274, 126, 5609])).
% 2.34/2.52 tff(7276,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[321, 7275, 255])).
% 2.34/2.52 tff(7277,plain,
% 2.34/2.52 (~b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6447, 7276, 7226, 7262, 7270, 7268])).
% 2.34/2.52 tff(7278,plain,
% 2.34/2.52 (r(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[293, 7277])).
% 2.34/2.52 tff(7279,plain,
% 2.34/2.52 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6081, 7278, 95, 7274])).
% 2.34/2.52 tff(7280,plain,
% 2.34/2.52 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[454, 7279, 254])).
% 2.34/2.52 tff(7281,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7282,plain,
% 2.34/2.52 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7283,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7282])).
% 2.34/2.52 tff(7284,plain,
% 2.34/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(transitivity,[status(thm)],[7283, 7281])).
% 2.34/2.52 tff(7285,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.52 inference(quant_inst,[status(thm)],[])).
% 2.34/2.52 tff(7286,plain,
% 2.34/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 2.34/2.52 tff(7287,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7286, 171, 3281, 7262, 7280, 7226, 7276])).
% 2.34/2.52 tff(7288,plain,((~r(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7289,plain,
% 2.34/2.52 (~r(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7288, 6500, 95, 61, 5609, 6972])).
% 2.34/2.52 tff(7290,plain,
% 2.34/2.52 (b(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[124, 7289])).
% 2.34/2.52 tff(7291,plain,
% 2.34/2.52 (~b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7045, 7290, 6972, 6500])).
% 2.34/2.52 tff(7292,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[244, 7291])).
% 2.34/2.52 tff(7293,plain,
% 2.34/2.52 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6984, 7292, 5609, 61])).
% 2.34/2.52 tff(7294,plain,
% 2.34/2.52 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[205, 7293])).
% 2.34/2.52 tff(7295,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7224, 5609, 6972, 95, 61])).
% 2.34/2.52 tff(7296,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[145, 7295])).
% 2.34/2.52 tff(7297,plain,
% 2.34/2.52 (~b(z, s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6997, 502, 161, 2, 95, 126])).
% 2.34/2.52 tff(7298,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[498, 7297, 5540])).
% 2.34/2.52 tff(7299,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7300,plain,
% 2.34/2.52 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7299, 7290, 7292, 95, 61])).
% 2.34/2.52 tff(7301,plain,
% 2.34/2.52 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[479, 7300])).
% 2.34/2.52 tff(7302,plain,
% 2.34/2.52 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6347, 7301, 6972, 7296, 7290, 7294])).
% 2.34/2.52 tff(7303,plain,
% 2.34/2.52 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[225, 7302])).
% 2.34/2.52 tff(7304,plain,
% 2.34/2.52 (~r(z, s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6331, 7303, 61, 95])).
% 2.34/2.52 tff(7305,plain,
% 2.34/2.52 (b(z, s(s(s(s(s(z))))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[498, 7304])).
% 2.34/2.52 tff(7306,plain,
% 2.34/2.52 (~b(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[179, 7294, 7296, 7290])).
% 2.34/2.52 tff(7307,plain,
% 2.34/2.52 (r(s(s(z)), z)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[157, 7306])).
% 2.34/2.52 tff(7308,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6095, 106, 2, 637, 95, 5567])).
% 2.34/2.52 tff(7309,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7310,plain,
% 2.34/2.52 (~r(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7309, 7292, 7307, 95])).
% 2.34/2.52 tff(7311,plain,
% 2.34/2.52 (b(z, s(s(s(s(z)))))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[293, 7310])).
% 2.34/2.52 tff(7312,plain,
% 2.34/2.52 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[6149, 263, 95, 7292])).
% 2.34/2.52 tff(7313,plain,
% 2.34/2.52 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[374, 7312, 355])).
% 2.34/2.52 tff(7314,plain,
% 2.34/2.52 (~r(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7288, 323, 95, 61, 5609, 6972])).
% 2.34/2.52 tff(7315,plain,
% 2.34/2.52 (b(z, s(s(z)))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[124, 7314])).
% 2.34/2.52 tff(7316,plain,
% 2.34/2.52 (~b(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7045, 161, 3281, 323])).
% 2.34/2.52 tff(7317,plain,
% 2.34/2.52 (r(s(s(z)), s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[244, 7316])).
% 2.34/2.52 tff(7318,plain,
% 2.34/2.52 (~(s(s(z)) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[3903, 258, 161])).
% 2.34/2.52 tff(7319,plain,
% 2.34/2.52 (b(z, elem!1) <=> b(z, s(z))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[1428])).
% 2.34/2.52 tff(7320,plain,
% 2.34/2.52 (b(z, s(z)) <=> b(z, elem!1)),
% 2.34/2.52 inference(symmetry,[status(thm)],[7319])).
% 2.34/2.52 tff(7321,plain,
% 2.34/2.52 (b(z, elem!1)),
% 2.34/2.52 inference(modus_ponens,[status(thm)],[3281, 7320])).
% 2.34/2.52 tff(7322,plain,
% 2.34/2.52 ($false),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[258, 7321])).
% 2.34/2.52 tff(7323,plain,((~(elem!1 = s(z))) | b(z, elem!1) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.52 tff(7324,plain,
% 2.34/2.52 (~(elem!1 = s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[7323, 258, 3281])).
% 2.34/2.52 tff(7325,plain,
% 2.34/2.52 (~(s(z) = elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[1439, 7324])).
% 2.34/2.52 tff(7326,plain,
% 2.34/2.52 (r(elem!1, s(z))),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[687, 4819, 7324])).
% 2.34/2.52 tff(7327,plain,
% 2.34/2.52 (~r(s(s(z)), elem!1)),
% 2.34/2.52 inference(unit_resolution,[status(thm)],[4663, 7326, 95, 2])).
% 2.34/2.52 tff(7328,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7329,plain,
% 2.34/2.52 (((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.52 inference(rewrite,[status(thm)],[])).
% 2.34/2.52 tff(7330,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 2.34/2.52 inference(monotonicity,[status(thm)],[7329])).
% 2.34/2.52 tff(7331,plain,
% 2.34/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7330, 7328])).
% 2.34/2.53 tff(7332,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(z)))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7333,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7332, 7331])).
% 2.34/2.53 tff(7334,plain,
% 2.34/2.53 (~r(elem!1, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7333, 106, 7326, 2, 95])).
% 2.34/2.53 tff(7335,plain,
% 2.34/2.53 ((~b(elem!1, s(z))) <=> (~b(z, s(z)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[678])).
% 2.34/2.53 tff(7336,plain,
% 2.34/2.53 (~b(z, s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[4819, 7335])).
% 2.34/2.53 tff(7337,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3281, 7336])).
% 2.34/2.53 tff(7338,plain,((~(z = elem!1)) | (~b(z, s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7339,plain,
% 2.34/2.53 (~(z = elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7338, 4819, 3281])).
% 2.34/2.53 tff(7340,plain,
% 2.34/2.53 (r(z, elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[651, 7339, 258])).
% 2.34/2.53 tff(7341,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7342,plain,
% 2.34/2.53 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7343,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7342])).
% 2.34/2.53 tff(7344,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7343, 7341])).
% 2.34/2.53 tff(7345,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7346,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7345, 7344])).
% 2.34/2.53 tff(7347,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7346, 106, 638, 730, 95, 1446])).
% 2.34/2.53 tff(7348,plain,((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7349,plain,
% 2.34/2.53 (~r(s(z), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7348, 7340, 7326, 95])).
% 2.34/2.53 tff(7350,plain,
% 2.34/2.53 (b(s(z), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1444, 7349, 7325])).
% 2.34/2.53 tff(7351,plain,
% 2.34/2.53 (~r(s(s(z)), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[646, 554, 638, 95])).
% 2.34/2.53 tff(7352,plain,
% 2.34/2.53 (~b(s(s(z)), z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[5918, 554, 95, 159, 2, 126])).
% 2.34/2.53 tff(7353,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[157, 7352, 7351])).
% 2.34/2.53 tff(7354,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7355,plain,
% 2.34/2.53 (~r(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7354, 7340, 159, 2, 61, 95])).
% 2.34/2.53 tff(7356,plain,
% 2.34/2.53 (b(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[550, 7355])).
% 2.34/2.53 tff(7357,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 2.34/2.53 tff(7358,plain,
% 2.34/2.53 (b(elem!1, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3154, 3738, 7357])).
% 2.34/2.53 tff(7359,plain,
% 2.34/2.53 (b(s(s(z)), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1416, 2116, 1570])).
% 2.34/2.53 tff(7360,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7361,plain,
% 2.34/2.53 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7362,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7361])).
% 2.34/2.53 tff(7363,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7362, 7360])).
% 2.34/2.53 tff(7364,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7365,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7364, 7363])).
% 2.34/2.53 tff(7366,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7365, 171, 323, 1421, 7359, 7358])).
% 2.34/2.53 tff(7367,plain,((s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7368,plain,
% 2.34/2.53 (s(s(z)) = elem!1),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7367, 7356, 7350, 7334, 7327])).
% 2.34/2.53 tff(7369,plain,
% 2.34/2.53 (r(s(s(z)), z) <=> r(elem!1, z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7368])).
% 2.34/2.53 tff(7370,plain,
% 2.34/2.53 (~b(z, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3903, 7368, 258])).
% 2.34/2.53 tff(7371,plain,
% 2.34/2.53 (r(z, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[124, 7370])).
% 2.34/2.53 tff(7372,plain,
% 2.34/2.53 (~(elem!1 = z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[697, 7339])).
% 2.34/2.53 tff(7373,plain,
% 2.34/2.53 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3725, 7350, 32])).
% 2.34/2.53 tff(7374,plain,
% 2.34/2.53 (~(s(elem!1) = s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[922, 7339])).
% 2.34/2.53 tff(7375,plain,
% 2.34/2.53 (~r(s(s(z)), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4663, 730, 95, 2])).
% 2.34/2.53 tff(7376,plain,
% 2.34/2.53 (~r(elem!1, s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7333, 106, 730, 2, 95])).
% 2.34/2.53 tff(7377,plain,
% 2.34/2.53 (~r(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7354, 638, 159, 2, 126, 95])).
% 2.34/2.53 tff(7378,plain,
% 2.34/2.53 (b(s(z), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[550, 7377])).
% 2.34/2.53 tff(7379,plain,
% 2.34/2.53 (s(s(z)) = elem!1),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7367, 7378, 1421, 7376, 7375])).
% 2.34/2.53 tff(7380,plain,
% 2.34/2.53 (s(s(s(z))) = s(elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7379])).
% 2.34/2.53 tff(7381,plain,
% 2.34/2.53 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7380])).
% 2.34/2.53 tff(7382,plain,
% 2.34/2.53 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7381])).
% 2.34/2.53 tff(7383,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7382])).
% 2.34/2.53 tff(7384,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7379])).
% 2.34/2.53 tff(7385,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(transitivity,[status(thm)],[7384, 7383])).
% 2.34/2.53 tff(7386,plain,
% 2.34/2.53 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[6049, 5324, 2, 3281, 126, 7378, 600])).
% 2.34/2.53 tff(7387,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[225, 7386])).
% 2.34/2.53 tff(7388,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7387, 7385])).
% 2.34/2.53 tff(7389,plain,
% 2.34/2.53 (r(s(z), s(s(s(s(s(z)))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7382])).
% 2.34/2.53 tff(7390,plain,
% 2.34/2.53 (r(s(z), s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[126, 7389])).
% 2.34/2.53 tff(7391,plain,
% 2.34/2.53 (~r(elem!1, z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4002, 152, 7379])).
% 2.34/2.53 tff(7392,plain,
% 2.34/2.53 (b(elem!1, z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1567, 7391, 3385])).
% 2.34/2.53 tff(7393,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7382])).
% 2.34/2.53 tff(7394,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[159, 7393])).
% 2.34/2.53 tff(7395,plain,
% 2.34/2.53 (s(s(z)) = elem!1),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7367, 1421, 323, 7357, 1570])).
% 2.34/2.53 tff(7396,plain,
% 2.34/2.53 (s(s(s(z))) = s(elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7395])).
% 2.34/2.53 tff(7397,plain,
% 2.34/2.53 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7396])).
% 2.34/2.53 tff(7398,plain,
% 2.34/2.53 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7397])).
% 2.34/2.53 tff(7399,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7398])).
% 2.34/2.53 tff(7400,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), z)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[159, 7399])).
% 2.34/2.53 tff(7401,plain,
% 2.34/2.53 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7398])).
% 2.34/2.53 tff(7402,plain,
% 2.34/2.53 (b(s(s(z)), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7395])).
% 2.34/2.53 tff(7403,plain,
% 2.34/2.53 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[160, 7402])).
% 2.34/2.53 tff(7404,plain,
% 2.34/2.53 (b(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7403, 7401])).
% 2.34/2.53 tff(7405,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7398])).
% 2.34/2.53 tff(7406,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7395])).
% 2.34/2.53 tff(7407,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[207, 7406])).
% 2.34/2.53 tff(7408,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), elem!1)),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7407, 7405])).
% 2.34/2.53 tff(7409,plain,
% 2.34/2.53 (~r(elem!1, z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[4002, 7395, 152])).
% 2.34/2.53 tff(7410,plain,
% 2.34/2.53 (b(elem!1, z)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1567, 7409, 3385])).
% 2.34/2.53 tff(7411,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7412,plain,
% 2.34/2.53 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7413,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7412])).
% 2.34/2.53 tff(7414,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7413, 7411])).
% 2.34/2.53 tff(7415,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7416,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7415, 7414])).
% 2.34/2.53 tff(7417,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7416, 171, 7410, 3281, 7408, 1421, 7404, 7400])).
% 2.34/2.53 tff(7418,plain,((~b(s(z), elem!1)) | (~b(z, 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))))))) | (elem!1 = z) | r(s(s(z)), z) | (~b(s(z), s(s(z)))) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7419,plain,
% 2.34/2.53 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7418, 7387, 159, 1421, 3281, 3385, 152, 7378, 7376, 7375])).
% 2.34/2.53 tff(7420,plain,
% 2.34/2.53 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[205, 7419])).
% 2.34/2.53 tff(7421,plain,
% 2.34/2.53 (r(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[3887, 7420, 7379])).
% 2.34/2.53 tff(7422,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3879])).
% 2.34/2.53 tff(7423,plain,
% 2.34/2.53 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[3879])).
% 2.34/2.53 tff(7424,plain,
% 2.34/2.53 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(symmetry,[status(thm)],[7423])).
% 2.34/2.53 tff(7425,plain,
% 2.34/2.53 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7424])).
% 2.34/2.53 tff(7426,plain,
% 2.34/2.53 (~b(elem!1, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7416, 171, 1596, 3281, 1516, 1421, 3914])).
% 2.34/2.53 tff(7427,plain,
% 2.34/2.53 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7426, 7425])).
% 2.34/2.53 tff(7428,plain,
% 2.34/2.53 (r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[782, 7427, 1908])).
% 2.34/2.53 tff(7429,plain,
% 2.34/2.53 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[777, 7428, 95, 730])).
% 2.34/2.53 tff(7430,plain,
% 2.34/2.53 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[479, 7429])).
% 2.34/2.53 tff(7431,plain,
% 2.34/2.53 (b(s(s(s(elem!1))), s(z))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7430, 7422])).
% 2.34/2.53 tff(7432,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7433,plain,
% 2.34/2.53 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7434,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7433])).
% 2.34/2.53 tff(7435,plain,
% 2.34/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7434, 7432])).
% 2.34/2.53 tff(7436,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7437,plain,
% 2.34/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7436, 7435])).
% 2.34/2.53 tff(7438,plain,
% 2.34/2.53 ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1)))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7437, 171, 1596, 3281, 1421, 3914])).
% 2.34/2.53 tff(7439,plain,
% 2.34/2.53 (~b(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7438, 7431])).
% 2.34/2.53 tff(7440,plain,
% 2.34/2.53 (r(z, s(s(s(elem!1))))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1593, 25, 7439, 3930])).
% 2.34/2.53 tff(7441,plain,
% 2.34/2.53 (~(s(elem!1) = elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1492, 1418])).
% 2.34/2.53 tff(7442,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 2.34/2.53 tff(7443,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7444,plain,
% 2.34/2.53 (((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7445,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))))),
% 2.34/2.53 inference(monotonicity,[status(thm)],[7444])).
% 2.34/2.53 tff(7446,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 2.34/2.53 inference(transitivity,[status(thm)],[7445, 7443])).
% 2.34/2.53 tff(7447,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)))),
% 2.34/2.53 inference(quant_inst,[status(thm)],[])).
% 2.34/2.53 tff(7448,plain,
% 2.34/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))),
% 2.34/2.53 inference(modus_ponens,[status(thm)],[7447, 7446])).
% 2.34/2.53 tff(7449,plain,
% 2.34/2.53 ($false),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7448, 106, 7442, 730, 1663, 95])).
% 2.34/2.53 tff(7450,plain,((~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.53 tff(7451,plain,
% 2.34/2.53 (~r(s(elem!1), elem!1)),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[7450, 1663, 95, 730])).
% 2.34/2.53 tff(7452,plain,
% 2.34/2.53 (r(elem!1, s(elem!1))),
% 2.34/2.53 inference(unit_resolution,[status(thm)],[1533, 7451, 1516, 1525, 1503])).
% 2.34/2.53 tff(7453,plain,
% 2.34/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.34/2.53 inference(rewrite,[status(thm)],[])).
% 2.34/2.53 tff(7454,plain,
% 2.34/2.53 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7455,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7454])).
% 2.34/2.54 tff(7456,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7455, 7453])).
% 2.34/2.54 tff(7457,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7458,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(elem!1), s(z)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7457, 7456])).
% 2.34/2.54 tff(7459,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7458, 106, 7452, 730, 1663, 2231])).
% 2.34/2.54 tff(7460,plain,((~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(elem!1) = elem!1) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7461,plain,
% 2.34/2.54 (~r(s(elem!1), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7460, 1525, 2231, 1516, 730, 1503, 95])).
% 2.34/2.54 tff(7462,plain,
% 2.34/2.54 (b(s(elem!1), s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1717, 7461, 701])).
% 2.34/2.54 tff(7463,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7464,plain,
% 2.34/2.54 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7465,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7464])).
% 2.34/2.54 tff(7466,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7465, 7463])).
% 2.34/2.54 tff(7467,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7468,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7467, 7466])).
% 2.34/2.54 tff(7469,plain,
% 2.34/2.54 (~b(s(z), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7468, 171, 1525, 1809, 7462, 1421])).
% 2.34/2.54 tff(7470,plain,
% 2.34/2.54 (r(s(z), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1861, 7469, 1821])).
% 2.34/2.54 tff(7471,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7472,plain,
% 2.34/2.54 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~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(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7473,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7472])).
% 2.34/2.54 tff(7474,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7473, 7471])).
% 2.34/2.54 tff(7475,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7476,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7475, 7474])).
% 2.34/2.54 tff(7477,plain,
% 2.34/2.54 (~b(s(elem!1), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7476, 171, 1596, 1525, 3281, 7462, 1516])).
% 2.34/2.54 tff(7478,plain,
% 2.34/2.54 (r(s(elem!1), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1523, 7477, 1503])).
% 2.34/2.54 tff(7479,plain,
% 2.34/2.54 (~r(z, s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1869, 7478, 95, 7470])).
% 2.34/2.54 tff(7480,plain,
% 2.34/2.54 (b(z, s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1679, 7479])).
% 2.34/2.54 tff(7481,plain,
% 2.34/2.54 (~r(s(elem!1), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1827, 7470, 95, 638])).
% 2.34/2.54 tff(7482,plain,
% 2.34/2.54 (b(s(elem!1), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1691, 7481])).
% 2.34/2.54 tff(7483,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7484,plain,
% 2.34/2.54 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7485,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7484])).
% 2.34/2.54 tff(7486,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7485, 7483])).
% 2.34/2.54 tff(7487,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7488,plain,
% 2.34/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), z))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 2.34/2.54 tff(7489,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7488, 171, 1525, 3281, 7482, 7480, 3914])).
% 2.34/2.54 tff(7490,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (s(elem!1) = elem!1) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7491,plain,
% 2.34/2.54 (~b(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7490, 1516, 3914, 95, 638, 7441, 1596, 3281, 7431, 1421, 701, 2231, 730])).
% 2.34/2.54 tff(7492,plain,
% 2.34/2.54 (r(s(s(s(elem!1))), s(elem!1))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1783, 7491, 3971])).
% 2.34/2.54 tff(7493,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7494,plain,
% 2.34/2.54 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7495,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7494])).
% 2.34/2.54 tff(7496,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7495, 7493])).
% 2.34/2.54 tff(7497,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7498,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7497, 7496])).
% 2.34/2.54 tff(7499,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7498, 106, 638, 7492, 1652, 7440])).
% 2.34/2.54 tff(7500,plain,((~b(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~(s(s(z)) = elem!1)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7501,plain,
% 2.34/2.54 (~b(s(s(s(elem!1))), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7500, 7421, 638, 7394, 95, 7392, 3281, 1421, 701, 7390, 730, 7379, 1908])).
% 2.34/2.54 tff(7502,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7501, 7388])).
% 2.34/2.54 tff(7503,plain,(r(s(s(z)), z) | (~r(z, elem!1)) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (s(elem!1) = s(z)) | (~r(elem!1, s(z))) | (elem!1 = s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (elem!1 = z) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7504,plain,
% 2.34/2.54 (r(s(s(z)), z)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7503, 7340, 95, 3281, 7350, 7374, 7326, 7373, 159, 7372, 2, 61, 7371])).
% 2.34/2.54 tff(7505,plain,
% 2.34/2.54 (r(elem!1, z)),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7504, 7369])).
% 2.34/2.54 tff(7506,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7507,plain,
% 2.34/2.54 (((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7508,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1))))),
% 2.34/2.54 inference(monotonicity,[status(thm)],[7507])).
% 2.34/2.54 tff(7509,plain,
% 2.34/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)))),
% 2.34/2.54 inference(transitivity,[status(thm)],[7508, 7506])).
% 2.34/2.54 tff(7510,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(elem!1, z)) | (~r(elem!1, s(z))))),
% 2.34/2.54 inference(quant_inst,[status(thm)],[])).
% 2.34/2.54 tff(7511,plain,
% 2.34/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1))),
% 2.34/2.54 inference(modus_ponens,[status(thm)],[7510, 7509])).
% 2.34/2.54 tff(7512,plain,
% 2.34/2.54 ($false),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7511, 106, 7340, 7505, 7326, 95])).
% 2.34/2.54 tff(7513,plain,(b(elem!1, s(z)) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(z))) | b(z, elem!1) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.54 tff(7514,plain,
% 2.34/2.54 (b(elem!1, s(z))),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[7513, 159, 3281, 95, 2, 258, 32])).
% 2.34/2.54 tff(7515,plain,
% 2.34/2.54 (r(z, elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[651, 3078, 258])).
% 2.34/2.54 tff(7516,plain,
% 2.34/2.54 (~b(s(s(z)), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[4888, 1421, 679, 323])).
% 2.34/2.54 tff(7517,plain,
% 2.34/2.54 (r(s(s(z)), elem!1)),
% 2.34/2.54 inference(unit_resolution,[status(thm)],[1416, 7516, 2116])).
% 2.34/2.54 tff(7518,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7519,plain,
% 2.34/2.54 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z))) <=> ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.34/2.54 inference(rewrite,[status(thm)],[])).
% 2.34/2.54 tff(7520,plain,
% 2.34/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7519])).
% 2.34/2.55 tff(7521,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7520, 7518])).
% 2.34/2.55 tff(7522,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, z)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7523,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7522, 7521])).
% 2.34/2.55 tff(7524,plain,
% 2.34/2.55 (~b(elem!1, z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7523, 171, 679, 3281, 1421])).
% 2.34/2.55 tff(7525,plain,
% 2.34/2.55 (r(elem!1, z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1567, 7524, 3385])).
% 2.34/2.55 tff(7526,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7527,plain,
% 2.34/2.55 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7528,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7527])).
% 2.34/2.55 tff(7529,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7528, 7526])).
% 2.34/2.55 tff(7530,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7531,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)) | (~r(z, elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7530, 7529])).
% 2.34/2.55 tff(7532,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7531, 106, 638, 1554, 637, 1403])).
% 2.34/2.55 tff(7533,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7534,plain,
% 2.34/2.55 (~r(s(s(z)), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7533, 7525, 638, 7517])).
% 2.34/2.55 tff(7535,plain,
% 2.34/2.55 (b(s(s(z)), z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[157, 7534])).
% 2.34/2.55 tff(7536,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7537,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7538,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7537, 7536])).
% 2.34/2.55 tff(7539,plain,
% 2.34/2.55 (~r(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7538, 106, 638, 7525, 7517])).
% 2.34/2.55 tff(7540,plain,
% 2.34/2.55 (b(z, s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[124, 7539])).
% 2.34/2.55 tff(7541,plain,
% 2.34/2.55 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[215, 7540, 159, 7535])).
% 2.34/2.55 tff(7542,plain,
% 2.34/2.55 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[225, 7541])).
% 2.34/2.55 tff(7543,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[5694, 7542, 61, 2])).
% 2.34/2.55 tff(7544,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[479, 7543])).
% 2.34/2.55 tff(7545,plain,
% 2.34/2.55 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[179, 7540, 159, 7535])).
% 2.34/2.55 tff(7546,plain,
% 2.34/2.55 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[205, 7545])).
% 2.34/2.55 tff(7547,plain,
% 2.34/2.55 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3767, 7546, 7517, 7542])).
% 2.34/2.55 tff(7548,plain,
% 2.34/2.55 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[782, 7547, 3726])).
% 2.34/2.55 tff(7549,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3777, 7548, 7544, 679, 1421])).
% 2.34/2.55 tff(7550,plain,((~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, elem!1)) | (elem!1 = z) | (~b(z, s(z))) | (s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7551,plain,
% 2.34/2.55 (~b(s(z), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7550, 7515, 2, 159, 7514, 3100, 3281, 2116, 323, 32])).
% 2.34/2.55 tff(7552,plain,
% 2.34/2.55 (r(s(z), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1444, 7551, 7325])).
% 2.34/2.55 tff(7553,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7554,plain,
% 2.34/2.55 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7555,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7554])).
% 2.34/2.55 tff(7556,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1)))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7555, 7553])).
% 2.34/2.55 tff(7557,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7558,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7557, 7556])).
% 2.34/2.55 tff(7559,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7558, 106, 638, 1554, 95, 1446])).
% 2.34/2.55 tff(7560,plain,((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7561,plain,
% 2.34/2.55 (~r(elem!1, z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7560, 7515, 95, 7552])).
% 2.34/2.55 tff(7562,plain,
% 2.34/2.55 (b(elem!1, z)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1567, 7561, 3100])).
% 2.34/2.55 tff(7563,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3664, 106, 638, 95, 1446, 769])).
% 2.34/2.55 tff(7564,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7565,plain,
% 2.34/2.55 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7564, 7515, 95, 7552])).
% 2.34/2.55 tff(7566,plain,
% 2.34/2.55 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(commutativity,[status(thm)],[])).
% 2.34/2.55 tff(7567,plain,
% 2.34/2.55 ((s(s(z)) = s(s(s(s(s(s(z))))))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.34/2.55 inference(symmetry,[status(thm)],[7566])).
% 2.34/2.55 tff(7568,plain,
% 2.34/2.55 ((~(s(s(z)) = s(s(s(s(s(s(z)))))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(z))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7567])).
% 2.34/2.55 tff(7569,plain,
% 2.34/2.55 (~(s(s(s(s(s(s(z)))))) = s(s(z)))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[3477, 7568])).
% 2.34/2.55 tff(7570,plain,
% 2.34/2.55 (r(s(s(s(s(s(s(z)))))), s(z)) <=> r(s(elem!1), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3085])).
% 2.34/2.55 tff(7571,plain,
% 2.34/2.55 (r(s(elem!1), s(z)) <=> r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[7570])).
% 2.34/2.55 tff(7572,plain,
% 2.34/2.55 (b(s(elem!1), s(z)) <=> b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[3084])).
% 2.34/2.55 tff(7573,plain,
% 2.34/2.55 (b(s(s(s(s(s(s(z)))))), s(z)) <=> b(s(elem!1), s(z))),
% 2.34/2.55 inference(symmetry,[status(thm)],[7572])).
% 2.34/2.55 tff(7574,plain,
% 2.34/2.55 ((~b(s(s(s(s(s(s(z)))))), s(z))) <=> (~b(s(elem!1), s(z)))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7573])).
% 2.34/2.55 tff(7575,plain,
% 2.34/2.55 (r(z, s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[3251, 3077, 638])).
% 2.34/2.55 tff(7576,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[6331, 7575, 126, 95])).
% 2.34/2.55 tff(7577,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[225, 7576])).
% 2.34/2.55 tff(7578,assumption,(s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.55 tff(7579,plain,
% 2.34/2.55 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z)))))),
% 2.34/2.55 inference(symmetry,[status(thm)],[7578])).
% 2.34/2.55 tff(7580,assumption,(~(s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))), introduced(assumption)).
% 2.34/2.55 tff(7581,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7580, 7579])).
% 2.34/2.55 tff(7582,plain,((~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7583,plain,
% 2.34/2.55 (~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7582, 3518])).
% 2.34/2.55 tff(7584,assumption,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.55 tff(7585,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7586,plain,
% 2.34/2.55 (((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7587,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7586])).
% 2.34/2.55 tff(7588,plain,
% 2.34/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7587, 7585])).
% 2.34/2.55 tff(7589,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7590,plain,
% 2.34/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7589, 7588])).
% 2.34/2.55 tff(7591,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7590, 106, 95, 126, 1288, 7584])).
% 2.34/2.55 tff(7592,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7593,plain,
% 2.34/2.55 (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7592, 7575, 126, 95])).
% 2.34/2.55 tff(7594,assumption,(~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.55 tff(7595,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.55 tff(7596,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.55 tff(7597,plain,
% 2.34/2.55 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7598,plain,
% 2.34/2.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7599,plain,
% 2.34/2.55 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7598, 7597])).
% 2.34/2.55 tff(7600,plain,
% 2.34/2.55 ($false),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7599, 25, 7596, 7595, 7594])).
% 2.34/2.55 tff(7601,plain,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))) | (s(s(s(s(s(z))))) = s(s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.55 tff(7602,plain,
% 2.34/2.55 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7601, 7593, 7583])).
% 2.34/2.55 tff(7603,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(z)))))), s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7604,plain,
% 2.34/2.55 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, 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(s(z)))))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(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(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(rewrite,[status(thm)],[])).
% 2.34/2.55 tff(7605,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, 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(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(z)))))), s(s(s(s(s(z)))))))))),
% 2.34/2.55 inference(monotonicity,[status(thm)],[7604])).
% 2.34/2.55 tff(7606,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, 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(s(z)))))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(z)))))), s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(transitivity,[status(thm)],[7605, 7603])).
% 2.34/2.55 tff(7607,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, 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(s(z)))))), s(s(s(s(s(z))))))))),
% 2.34/2.55 inference(quant_inst,[status(thm)],[])).
% 2.34/2.55 tff(7608,plain,
% 2.34/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(z)))))), s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7607, 7606])).
% 2.34/2.55 tff(7609,plain,
% 2.34/2.55 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z)))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7608, 171, 323, 3281, 207, 159])).
% 2.34/2.55 tff(7610,plain,
% 2.34/2.55 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(s(z))))))),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[7609, 3593])).
% 2.34/2.55 tff(7611,plain,
% 2.34/2.55 (~b(s(elem!1), elem!1)),
% 2.34/2.55 inference(modus_ponens,[status(thm)],[7610, 3604])).
% 2.34/2.55 tff(7612,plain,
% 2.34/2.55 (r(s(elem!1), elem!1)),
% 2.34/2.55 inference(unit_resolution,[status(thm)],[1523, 7611, 3519])).
% 2.34/2.55 tff(7613,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.55 tff(7614,plain,
% 2.34/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7615,plain,
% 2.34/2.56 (((~b(z, s(z))) | (~b(z, 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(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, 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)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7616,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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))))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7615])).
% 2.34/2.56 tff(7617,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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)))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7616, 7614])).
% 2.34/2.56 tff(7618,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(z)))))), 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)))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7619,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7618, 7617])).
% 2.34/2.56 tff(7620,plain,
% 2.34/2.56 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(z, s(s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7619, 171, 3281, 159, 7613])).
% 2.34/2.56 tff(7621,plain,
% 2.34/2.56 (~b(z, s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7620, 3593])).
% 2.34/2.56 tff(7622,plain,
% 2.34/2.56 (~b(z, s(elem!1))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7621, 3590])).
% 2.34/2.56 tff(7623,plain,
% 2.34/2.56 (r(z, s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1679, 7622])).
% 2.34/2.56 tff(7624,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1869, 7623, 7612, 95, 1822])).
% 2.34/2.56 tff(7625,plain,((~r(s(z), s(elem!1))) | (~r(s(z), z)) | (~(elem!1 = s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7626,plain,
% 2.34/2.56 (~r(s(z), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7625, 3077, 95, 3281, 159, 7602, 323, 7577, 638])).
% 2.34/2.56 tff(7627,plain,
% 2.34/2.56 (b(s(z), s(elem!1))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1832, 7626, 1821])).
% 2.34/2.56 tff(7628,plain,
% 2.34/2.56 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[1834, 3305])).
% 2.34/2.56 tff(7629,assumption,(~b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.56 tff(7630,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7629, 7628])).
% 2.34/2.56 tff(7631,plain,(b(s(z), s(s(s(s(s(s(z))))))) | (~b(s(z), s(elem!1))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7632,plain,
% 2.34/2.56 (b(s(z), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7631, 7627, 3077])).
% 2.34/2.56 tff(7633,plain,
% 2.34/2.56 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[5251, 3077, 679])).
% 2.34/2.56 tff(7634,assumption,(b(s(z), s(s(s(s(s(s(z)))))))), introduced(assumption)).
% 2.34/2.56 tff(7635,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7636,plain,
% 2.34/2.56 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7637,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7636])).
% 2.34/2.56 tff(7638,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7637, 7635])).
% 2.34/2.56 tff(7639,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7640,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7639, 7638])).
% 2.34/2.56 tff(7641,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7640, 171, 323, 4, 3541, 7613, 7634])).
% 2.34/2.56 tff(7642,plain,((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7643,plain,
% 2.34/2.56 (~b(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7642, 7633, 323, 7602, 7632])).
% 2.34/2.56 tff(7644,plain,
% 2.34/2.56 (~b(s(elem!1), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7643, 7574])).
% 2.34/2.56 tff(7645,plain,
% 2.34/2.56 (r(s(elem!1), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[1717, 7644, 701])).
% 2.34/2.56 tff(7646,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7645, 7571])).
% 2.34/2.56 tff(7647,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7648,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7649,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 2.34/2.56 tff(7650,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7649, 106, 2, 95, 7646])).
% 2.34/2.56 tff(7651,plain,
% 2.34/2.56 (((~![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))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7652,plain,
% 2.34/2.56 ((~![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))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7653,plain,
% 2.34/2.56 ((~![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)))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7652, 7651])).
% 2.34/2.56 tff(7654,plain,
% 2.34/2.56 ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7653, 25, 7650])).
% 2.34/2.56 tff(7655,plain,
% 2.34/2.56 (b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7654, 7569])).
% 2.34/2.56 tff(7656,plain,
% 2.34/2.56 (r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[1663, 7571])).
% 2.34/2.56 tff(7657,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7658,plain,
% 2.34/2.56 (((~r(s(z), z)) | (~r(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(z))))))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7659,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7658])).
% 2.34/2.56 tff(7660,plain,
% 2.34/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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(z)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7659, 7657])).
% 2.34/2.56 tff(7661,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(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(z)))))))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7662,plain,
% 2.34/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(z)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7661, 7660])).
% 2.34/2.56 tff(7663,plain,
% 2.34/2.56 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7662, 106, 2, 95, 3572])).
% 2.34/2.56 tff(7664,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7663, 7656])).
% 2.34/2.56 tff(7665,plain,((~r(s(elem!1), s(z))) | (~(elem!1 = s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(s(s(s(s(z))))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7666,plain,
% 2.34/2.56 (~r(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7665, 7645, 2, 95, 3077])).
% 2.34/2.56 tff(7667,plain,
% 2.34/2.56 (b(s(s(z)), s(s(s(s(s(s(z)))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[3634, 7666, 3477])).
% 2.34/2.56 tff(7668,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7669,plain,
% 2.34/2.56 (((~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(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7670,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7669])).
% 2.34/2.56 tff(7671,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7670, 7668])).
% 2.34/2.56 tff(7672,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(z), s(s(z)))))),
% 2.34/2.56 inference(quant_inst,[status(thm)],[])).
% 2.34/2.56 tff(7673,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(z)))))))) | (~b(s(s(s(s(s(s(z)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(z))))))))),
% 2.34/2.56 inference(modus_ponens,[status(thm)],[7672, 7671])).
% 2.34/2.56 tff(7674,plain,
% 2.34/2.56 ($false),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7673, 171, 323, 7667, 7632, 7655])).
% 2.34/2.56 tff(7675,plain,((~(elem!1 = s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (s(elem!1) = s(z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(z, elem!1)) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.56 tff(7676,plain,
% 2.34/2.56 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[7675, 701, 2, 95, 323, 3281, 159, 7515, 61, 7514])).
% 2.34/2.56 tff(7677,plain,
% 2.34/2.56 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.56 inference(unit_resolution,[status(thm)],[782, 7676, 7565])).
% 2.34/2.56 tff(7678,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7679,plain,
% 2.34/2.56 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z))) <=> ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.56 inference(rewrite,[status(thm)],[])).
% 2.34/2.56 tff(7680,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.56 inference(monotonicity,[status(thm)],[7679])).
% 2.34/2.56 tff(7681,plain,
% 2.34/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.56 inference(transitivity,[status(thm)],[7680, 7678])).
% 2.34/2.56 tff(7682,plain,
% 2.34/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7683,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7682, 7681])).
% 2.34/2.57 tff(7684,plain,
% 2.34/2.57 ((~b(elem!1, z)) | (~b(z, s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7683, 171, 3281, 7677, 159])).
% 2.34/2.57 tff(7685,plain,
% 2.34/2.57 (~b(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7684, 7562])).
% 2.34/2.57 tff(7686,plain,
% 2.34/2.57 (r(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[498, 7685])).
% 2.34/2.57 tff(7687,plain,
% 2.34/2.57 ((~(elem!1 = s(s(s(s(s(z))))))) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[760])).
% 2.34/2.57 tff(7688,plain,
% 2.34/2.57 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7676, 7687])).
% 2.34/2.57 tff(7689,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4046, 106, 638, 2463, 95, 1446])).
% 2.34/2.57 tff(7690,plain,((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7691,plain,
% 2.34/2.57 (~r(elem!1, s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7690, 7515, 95, 7552])).
% 2.34/2.57 tff(7692,plain,
% 2.34/2.57 (b(elem!1, s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3154, 7691, 3738])).
% 2.34/2.57 tff(7693,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7694,plain,
% 2.34/2.57 (((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7695,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7694])).
% 2.34/2.57 tff(7696,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7695, 7693])).
% 2.34/2.57 tff(7697,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), elem!1)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7698,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7697, 7696])).
% 2.34/2.57 tff(7699,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7698, 171, 1596, 323, 3281, 4176, 839, 159])).
% 2.34/2.57 tff(7700,plain,((~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7701,plain,
% 2.34/2.57 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7700, 7692, 323, 3281, 7562, 159])).
% 2.34/2.57 tff(7702,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[853, 7701, 7688])).
% 2.34/2.57 tff(7703,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7704,plain,
% 2.34/2.57 (((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7705,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7704])).
% 2.34/2.57 tff(7706,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7705, 7703])).
% 2.34/2.57 tff(7707,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), elem!1)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7708,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7707, 7706])).
% 2.34/2.57 tff(7709,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7708, 106, 95, 7702, 61, 7686])).
% 2.34/2.57 tff(7710,plain,((s(elem!1) = s(z)) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(z))) | (s(s(z)) = elem!1) | b(s(z), s(s(s(s(s(z)))))) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7711,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7710, 7318, 258, 95, 3281, 7317, 701, 159, 32, 323])).
% 2.34/2.57 tff(7712,plain,(b(z, elem!1) | (~r(s(z), z)) | (~b(z, s(z))) | (s(elem!1) = s(z)) | (~b(s(s(s(s(s(z))))), z)) | b(s(z), s(s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7713,plain,
% 2.34/2.57 (s(elem!1) = s(z)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7712, 258, 6972, 95, 7296, 32, 323, 7315])).
% 2.34/2.57 tff(7714,plain,
% 2.34/2.57 (z = elem!1),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[922, 7713])).
% 2.34/2.57 tff(7715,plain,
% 2.34/2.57 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7714])).
% 2.34/2.57 tff(7716,plain,
% 2.34/2.57 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.34/2.57 inference(symmetry,[status(thm)],[7715])).
% 2.34/2.57 tff(7717,plain,
% 2.34/2.57 ((~r(s(s(z)), elem!1)) <=> (~r(s(s(z)), z))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7716])).
% 2.34/2.57 tff(7718,plain,
% 2.34/2.57 (~b(s(s(z)), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7045, 7315, 6972, 323])).
% 2.34/2.57 tff(7719,plain,
% 2.34/2.57 (r(s(s(z)), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[244, 7718])).
% 2.34/2.57 tff(7720,plain,
% 2.34/2.57 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6984, 7719, 5609, 61])).
% 2.34/2.57 tff(7721,plain,
% 2.34/2.57 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[205, 7720])).
% 2.34/2.57 tff(7722,plain,
% 2.34/2.57 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7299, 7315, 7719, 95, 61])).
% 2.34/2.57 tff(7723,plain,
% 2.34/2.57 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[479, 7722])).
% 2.34/2.57 tff(7724,plain,
% 2.34/2.57 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6347, 7723, 6972, 7296, 7315, 7721])).
% 2.34/2.57 tff(7725,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[225, 7724])).
% 2.34/2.57 tff(7726,plain,
% 2.34/2.57 (~r(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[6331, 7725, 61, 95])).
% 2.34/2.57 tff(7727,plain,
% 2.34/2.57 (b(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[498, 7726])).
% 2.34/2.57 tff(7728,plain,
% 2.34/2.57 (~(elem!1 = s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7323, 258, 6972])).
% 2.34/2.57 tff(7729,plain,
% 2.34/2.57 (b(z, elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7712, 6571, 6972, 95, 7296, 32, 323, 7315])).
% 2.34/2.57 tff(7730,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7731,plain,
% 2.34/2.57 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7732,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7731])).
% 2.34/2.57 tff(7733,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7732, 7730])).
% 2.34/2.57 tff(7734,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7735,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7734, 7733])).
% 2.34/2.57 tff(7736,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7735, 171, 3137, 679, 3281, 1421])).
% 2.34/2.57 tff(7737,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7738,plain,
% 2.34/2.57 (~b(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7737, 7729, 6972, 6539])).
% 2.34/2.57 tff(7739,plain,
% 2.34/2.57 (r(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[687, 7738, 1437])).
% 2.34/2.57 tff(7740,plain,
% 2.34/2.57 (~r(s(s(z)), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4663, 7739, 95, 7719])).
% 2.34/2.57 tff(7741,plain,
% 2.34/2.57 (~(elem!1 = s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4876, 2208, 4873])).
% 2.34/2.57 tff(7742,plain,
% 2.34/2.57 (~(s(z) = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1439, 7741])).
% 2.34/2.57 tff(7743,plain,
% 2.34/2.57 (b(s(z), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1444, 7742, 1924])).
% 2.34/2.57 tff(7744,plain,
% 2.34/2.57 (r(elem!1, s(s(z)))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7367, 7743, 2116, 323, 1570])).
% 2.34/2.57 tff(7745,plain,
% 2.34/2.57 (r(s(s(z)), s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[244, 4873])).
% 2.34/2.57 tff(7746,plain,
% 2.34/2.57 (r(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[687, 7741, 4819])).
% 2.34/2.57 tff(7747,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7333, 106, 7746, 7745, 7744, 95])).
% 2.34/2.57 tff(7748,plain,(r(s(s(z)), elem!1) | (~r(s(z), z)) | (s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | r(s(z), elem!1) | b(elem!1, s(z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7749,plain,
% 2.34/2.57 (s(s(z)) = elem!1),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7748, 7740, 95, 7718, 323, 1924, 7738])).
% 2.34/2.57 tff(7750,plain,
% 2.34/2.57 (s(s(s(z))) = s(elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7749])).
% 2.34/2.57 tff(7751,plain,
% 2.34/2.57 (s(s(s(s(z)))) = s(s(elem!1))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7750])).
% 2.34/2.57 tff(7752,plain,
% 2.34/2.57 (s(s(s(s(s(z))))) = s(s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7751])).
% 2.34/2.57 tff(7753,plain,
% 2.34/2.57 (b(s(s(s(s(s(z))))), z) <=> b(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7752])).
% 2.34/2.57 tff(7754,plain,
% 2.34/2.57 (b(s(s(s(elem!1))), z)),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7296, 7753])).
% 2.34/2.57 tff(7755,plain,
% 2.34/2.57 (b(z, s(s(s(s(s(z)))))) <=> b(z, s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7752])).
% 2.34/2.57 tff(7756,plain,
% 2.34/2.57 (b(z, s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[1313, 7755])).
% 2.34/2.57 tff(7757,plain,
% 2.34/2.57 (b(elem!1, s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7752])).
% 2.34/2.57 tff(7758,plain,
% 2.34/2.57 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[4821, 4819, 4])).
% 2.34/2.57 tff(7759,plain,
% 2.34/2.57 (r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[782, 7758, 6721])).
% 2.34/2.57 tff(7760,plain,
% 2.34/2.57 (r(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[687, 4819, 1437])).
% 2.34/2.57 tff(7761,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7762,plain,
% 2.34/2.57 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7763,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7762])).
% 2.34/2.57 tff(7764,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7763, 7761])).
% 2.34/2.57 tff(7765,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(z))))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7766,plain,
% 2.34/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7765, 7764])).
% 2.34/2.57 tff(7767,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7766, 106, 7760, 5609, 7759, 126])).
% 2.34/2.57 tff(7768,plain,(b(elem!1, s(z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))) | b(elem!1, s(s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7769,plain,
% 2.34/2.57 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7768, 7738, 61, 5609, 4, 1437])).
% 2.34/2.57 tff(7770,plain,
% 2.34/2.57 (b(elem!1, s(s(s(elem!1))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7769, 7757])).
% 2.34/2.57 tff(7771,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7772,plain,
% 2.34/2.57 (((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.57 inference(rewrite,[status(thm)],[])).
% 2.34/2.57 tff(7773,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7772])).
% 2.34/2.57 tff(7774,plain,
% 2.34/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7773, 7771])).
% 2.34/2.57 tff(7775,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, elem!1)))),
% 2.34/2.57 inference(quant_inst,[status(thm)],[])).
% 2.34/2.57 tff(7776,plain,
% 2.34/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)) | (~b(z, s(s(s(elem!1)))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7775, 7774])).
% 2.34/2.57 tff(7777,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7776, 171, 7729, 7770, 7756, 7754])).
% 2.34/2.57 tff(7778,plain,(r(s(z), elem!1) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (elem!1 = s(z)) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7779,plain,
% 2.34/2.57 (r(s(z), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7778, 7728, 95, 323, 5609, 7723, 7727, 32])).
% 2.34/2.57 tff(7780,plain,
% 2.34/2.57 (b(elem!1, s(z))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7513, 258, 6972, 95, 7296, 7719, 32])).
% 2.34/2.57 tff(7781,plain,
% 2.34/2.57 (~(s(s(z)) = elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[3903, 258, 7315])).
% 2.34/2.57 tff(7782,plain,
% 2.34/2.57 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.34/2.57 inference(monotonicity,[status(thm)],[923])).
% 2.34/2.57 tff(7783,plain,
% 2.34/2.57 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.34/2.57 inference(transitivity,[status(thm)],[7782, 759])).
% 2.34/2.57 tff(7784,plain,
% 2.34/2.57 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[7783])).
% 2.34/2.57 tff(7785,plain,
% 2.34/2.57 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[140, 7784])).
% 2.34/2.57 tff(7786,plain,
% 2.34/2.57 (r(z, s(s(s(s(s(z)))))) <=> r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[672])).
% 2.34/2.57 tff(7787,plain,
% 2.34/2.57 (r(elem!1, s(s(s(s(s(z)))))) <=> r(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(symmetry,[status(thm)],[7786])).
% 2.34/2.57 tff(7788,plain,
% 2.34/2.57 (r(z, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[769, 7787])).
% 2.34/2.57 tff(7789,plain,
% 2.34/2.57 ($false),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[493, 7788])).
% 2.34/2.57 tff(7790,plain,((~r(elem!1, s(s(s(s(s(z))))))) | r(z, s(s(s(s(s(z)))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.57 tff(7791,plain,
% 2.34/2.57 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[7790, 6332, 923])).
% 2.34/2.57 tff(7792,plain,
% 2.34/2.57 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[782, 7791, 7785])).
% 2.34/2.57 tff(7793,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[711])).
% 2.34/2.57 tff(7794,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.34/2.57 inference(symmetry,[status(thm)],[7793])).
% 2.34/2.57 tff(7795,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[396, 7794])).
% 2.34/2.57 tff(7796,plain,
% 2.34/2.57 (r(s(z), elem!1)),
% 2.34/2.57 inference(unit_resolution,[status(thm)],[1927, 923, 95])).
% 2.34/2.57 tff(7797,assumption,(r(s(s(s(s(s(z))))), s(s(elem!1)))), introduced(assumption)).
% 2.34/2.57 tff(7798,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(elem!1)))),
% 2.34/2.57 inference(monotonicity,[status(thm)],[1270])).
% 2.34/2.57 tff(7799,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.57 inference(symmetry,[status(thm)],[7798])).
% 2.34/2.57 tff(7800,plain,
% 2.34/2.57 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.57 inference(modus_ponens,[status(thm)],[7797, 7799])).
% 2.34/2.57 tff(7801,plain,
% 2.34/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7802,plain,
% 2.34/2.58 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7803,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7802])).
% 2.34/2.58 tff(7804,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7803, 7801])).
% 2.34/2.58 tff(7805,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(7806,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7805, 7804])).
% 2.34/2.58 tff(7807,plain,
% 2.34/2.58 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7806, 106, 2, 2463, 769])).
% 2.34/2.58 tff(7808,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7807, 7800])).
% 2.34/2.58 tff(7809,plain,((~r(s(s(s(s(s(z))))), s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7810,plain,
% 2.34/2.58 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7809, 2463, 2, 710, 7797])).
% 2.34/2.58 tff(7811,plain,
% 2.34/2.58 (b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[782, 7810, 7785])).
% 2.34/2.58 tff(7812,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7813,plain,
% 2.34/2.58 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7814,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7813])).
% 2.34/2.58 tff(7815,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7814, 7812])).
% 2.34/2.58 tff(7816,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), elem!1)))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(7817,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7816, 7815])).
% 2.34/2.58 tff(7818,plain,
% 2.34/2.58 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7817, 171, 679, 839, 160])).
% 2.34/2.58 tff(7819,plain,
% 2.34/2.58 (~b(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7818, 7811])).
% 2.34/2.58 tff(7820,plain,
% 2.34/2.58 (r(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[1416, 7819, 2116])).
% 2.34/2.58 tff(7821,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7822,plain,
% 2.34/2.58 (((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7823,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7822])).
% 2.34/2.58 tff(7824,plain,
% 2.34/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7823, 7821])).
% 2.34/2.58 tff(7825,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(7826,plain,
% 2.34/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7825, 7824])).
% 2.34/2.58 tff(7827,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7826, 106, 2, 2463, 1446, 7820])).
% 2.34/2.58 tff(7828,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7829,plain,
% 2.34/2.58 (~r(elem!1, s(s(z)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7828, 5686, 7796, 2116, 679, 839, 2, 710, 7795])).
% 2.34/2.58 tff(7830,plain,
% 2.34/2.58 (b(elem!1, s(s(z)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3154, 7829, 3738])).
% 2.34/2.58 tff(7831,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7832,plain,
% 2.34/2.58 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7833,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7832])).
% 2.34/2.58 tff(7834,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7833, 7831])).
% 2.34/2.58 tff(7835,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(7836,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7835, 7834])).
% 2.34/2.58 tff(7837,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7836, 171, 7830, 7792, 839, 5686])).
% 2.34/2.58 tff(7838,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), elem!1)) | (s(s(z)) = elem!1) | (~b(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7839,plain,
% 2.34/2.58 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7838, 7781, 7719, 7725, 7780, 7713, 61, 95])).
% 2.34/2.58 tff(7840,plain,
% 2.34/2.58 (r(s(s(s(s(s(z))))), z)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[2027, 4361])).
% 2.34/2.58 tff(7841,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[137, 7840])).
% 2.34/2.58 tff(7842,plain,((~r(s(s(s(s(s(z))))), elem!1)) | r(s(s(s(s(s(z))))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7843,plain,
% 2.34/2.58 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7842, 7714, 7295])).
% 2.34/2.58 tff(7844,plain,
% 2.34/2.58 (s(s(s(s(s(z))))) = elem!1),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[853, 7843, 7839])).
% 2.34/2.58 tff(7845,assumption,(s(s(s(s(s(z))))) = elem!1), introduced(assumption)).
% 2.34/2.58 tff(7846,plain,
% 2.34/2.58 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7845])).
% 2.34/2.58 tff(7847,plain,
% 2.34/2.58 (r(elem!1, s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.58 inference(symmetry,[status(thm)],[7846])).
% 2.34/2.58 tff(7848,plain,
% 2.34/2.58 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7847])).
% 2.34/2.58 tff(7849,plain,
% 2.34/2.58 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7357, 7848])).
% 2.34/2.58 tff(7850,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[396, 7849])).
% 2.34/2.58 tff(7851,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7852,plain,
% 2.34/2.58 (r(elem!1, s(s(z)))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7851, 7844, 7725])).
% 2.34/2.58 tff(7853,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7826, 106, 2, 2463, 1446, 1403])).
% 2.34/2.58 tff(7854,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7855,plain,
% 2.34/2.58 (~r(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7854, 7852, 7719, 7779])).
% 2.34/2.58 tff(7856,plain,
% 2.34/2.58 (~r(s(s(z)), z)),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7855, 7717])).
% 2.34/2.58 tff(7857,plain,
% 2.34/2.58 (~b(s(s(z)), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[179, 7721, 7296, 7315])).
% 2.34/2.58 tff(7858,plain,
% 2.34/2.58 (r(s(s(z)), z)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[157, 7857])).
% 2.34/2.58 tff(7859,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7858, 7856])).
% 2.34/2.58 tff(7860,plain,(b(z, elem!1) | (~r(s(z), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7861,plain,
% 2.34/2.58 (b(z, elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7860, 6500, 95, 5609, 32])).
% 2.34/2.58 tff(7862,plain,
% 2.34/2.58 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6885, 263, 61, 5609])).
% 2.34/2.58 tff(7863,plain,
% 2.34/2.58 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[3668, 7862])).
% 2.34/2.58 tff(7864,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7865,plain,
% 2.34/2.58 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), 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(z, elem!1)) | (~b(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(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.58 inference(rewrite,[status(thm)],[])).
% 2.34/2.58 tff(7866,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[7865])).
% 2.34/2.58 tff(7867,plain,
% 2.34/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7866, 7864])).
% 2.34/2.58 tff(7868,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), 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)))))),
% 2.34/2.58 inference(quant_inst,[status(thm)],[])).
% 2.34/2.58 tff(7869,plain,
% 2.34/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[7868, 7867])).
% 2.34/2.58 tff(7870,plain,
% 2.34/2.58 ($false),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7869, 171, 3137, 666, 3686, 160, 159, 356])).
% 2.34/2.58 tff(7871,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~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(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.58 tff(7872,plain,
% 2.34/2.58 (~b(s(s(z)), elem!1)),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[7871, 7863, 7861, 7294, 7296, 7313])).
% 2.34/2.58 tff(7873,plain,
% 2.34/2.58 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5932, 7313, 7296, 7290, 6972, 7301])).
% 2.34/2.58 tff(7874,plain,
% 2.34/2.58 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[454, 7873, 254])).
% 2.34/2.58 tff(7875,plain,
% 2.34/2.58 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[5981, 7313, 7290, 7311])).
% 2.34/2.58 tff(7876,plain,
% 2.34/2.58 (r(s(s(z)), s(s(s(s(z)))))),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[351, 7875])).
% 2.34/2.58 tff(7877,plain,
% 2.34/2.58 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[2358])).
% 2.34/2.58 tff(7878,plain,
% 2.34/2.58 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.58 inference(symmetry,[status(thm)],[7877])).
% 2.34/2.58 tff(7879,plain,
% 2.34/2.58 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.34/2.58 inference(monotonicity,[status(thm)],[2361])).
% 2.34/2.58 tff(7880,plain,
% 2.34/2.58 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.58 inference(transitivity,[status(thm)],[7879, 7878])).
% 2.34/2.58 tff(7881,plain,
% 2.34/2.58 (r(s(elem!1), s(s(s(elem!1))))),
% 2.34/2.58 inference(modus_ponens,[status(thm)],[500, 7880])).
% 2.34/2.58 tff(7882,plain,
% 2.34/2.58 (s(z) = elem!1),
% 2.34/2.58 inference(unit_resolution,[status(thm)],[6783, 1428])).
% 2.34/2.59 tff(7883,plain,
% 2.34/2.59 (r(elem!1, s(s(s(elem!1))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2894, 7882, 3])).
% 2.34/2.59 tff(7884,plain,
% 2.34/2.59 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[1428])).
% 2.34/2.59 tff(7885,plain,
% 2.34/2.59 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 2.34/2.59 inference(symmetry,[status(thm)],[7884])).
% 2.34/2.59 tff(7886,plain,
% 2.34/2.59 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[2358])).
% 2.34/2.59 tff(7887,plain,
% 2.34/2.59 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 2.34/2.59 inference(symmetry,[status(thm)],[7886])).
% 2.34/2.59 tff(7888,plain,
% 2.34/2.59 (r(s(s(z)), s(z)) <=> r(s(elem!1), elem!1)),
% 2.34/2.59 inference(transitivity,[status(thm)],[7887, 7885])).
% 2.34/2.59 tff(7889,plain,
% 2.34/2.59 (r(s(elem!1), elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[2, 7888])).
% 2.34/2.59 tff(7890,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(symmetry,[status(thm)],[4101])).
% 2.34/2.59 tff(7891,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.34/2.59 inference(symmetry,[status(thm)],[4100])).
% 2.34/2.59 tff(7892,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(transitivity,[status(thm)],[7891, 7890])).
% 2.34/2.59 tff(7893,plain,
% 2.34/2.59 (r(s(s(s(elem!1))), elem!1)),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[263, 7892])).
% 2.34/2.59 tff(7894,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1733, 7893, 7889, 7883, 7881])).
% 2.34/2.59 tff(7895,plain,((~(elem!1 = s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7896,plain,
% 2.34/2.59 (~(elem!1 = s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7895, 7876, 263, 7292, 7874])).
% 2.34/2.59 tff(7897,plain,
% 2.34/2.59 (b(z, elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7860, 323, 95, 5609, 32])).
% 2.34/2.59 tff(7898,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3419, 7358, 7359, 161, 3137])).
% 2.34/2.59 tff(7899,plain,((s(s(z)) = elem!1) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | r(elem!1, s(s(z))) | r(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7900,plain,
% 2.34/2.59 (r(elem!1, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7899, 7375, 161, 3137, 2116])).
% 2.34/2.59 tff(7901,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7333, 106, 730, 2, 7900, 95])).
% 2.34/2.59 tff(7902,plain,((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7903,plain,
% 2.34/2.59 (~r(elem!1, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7902, 2116, 95, 7315, 7897, 7719])).
% 2.34/2.59 tff(7904,plain,
% 2.34/2.59 (r(s(z), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7778, 1437, 95, 323, 5609, 7723, 7727, 32])).
% 2.34/2.59 tff(7905,plain,
% 2.34/2.59 (~r(elem!1, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7854, 7904, 7719, 1403])).
% 2.34/2.59 tff(7906,plain,
% 2.34/2.59 (b(elem!1, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3154, 7905, 3122])).
% 2.34/2.59 tff(7907,plain,
% 2.34/2.59 (~(s(elem!1) = s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5352, 7897])).
% 2.34/2.59 tff(7908,plain,
% 2.34/2.59 (~(z = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[703, 7907])).
% 2.34/2.59 tff(7909,plain,
% 2.34/2.59 (~(elem!1 = z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[697, 7908])).
% 2.34/2.59 tff(7910,plain,
% 2.34/2.59 (~r(elem!1, z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[4864, 7904, 7719, 1403])).
% 2.34/2.59 tff(7911,plain,
% 2.34/2.59 (b(elem!1, z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[1567, 7910, 7909])).
% 2.34/2.59 tff(7912,plain,
% 2.34/2.59 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7700, 7911, 6972, 323, 7906, 7296])).
% 2.34/2.59 tff(7913,plain,
% 2.34/2.59 (b(elem!1, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[687, 1437, 676])).
% 2.34/2.59 tff(7914,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7915,plain,
% 2.34/2.59 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7916,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[7915])).
% 2.34/2.59 tff(7917,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.34/2.59 inference(transitivity,[status(thm)],[7916, 7914])).
% 2.34/2.59 tff(7918,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(z))))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(7919,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7918, 7917])).
% 2.34/2.59 tff(7920,plain,
% 2.34/2.59 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7919, 171, 7897, 7911, 7913, 7723, 7296])).
% 2.34/2.59 tff(7921,plain,
% 2.34/2.59 (elem!1 = s(s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6735, 7920, 7904, 61, 7912])).
% 2.34/2.59 tff(7922,plain,
% 2.34/2.59 (s(s(s(s(s(z))))) = elem!1),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7921, 760])).
% 2.34/2.59 tff(7923,plain,
% 2.34/2.59 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7851, 7905, 7725])).
% 2.34/2.59 tff(7924,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7923, 7922])).
% 2.34/2.59 tff(7925,plain,((elem!1 = s(z)) | (~b(s(z), s(s(z)))) | (elem!1 = s(s(z))) | (~r(s(s(z)), elem!1)) | r(elem!1, s(z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7926,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7925, 3727, 3738, 323, 1437, 7903, 95, 5609, 32])).
% 2.34/2.59 tff(7927,plain,((s(s(z)) = elem!1) | (~b(s(z), s(s(z)))) | (elem!1 = s(z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z)))))) | b(s(s(z)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7928,plain,
% 2.34/2.59 (s(s(z)) = elem!1),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7927, 7896, 6500, 95, 5609, 32, 7872])).
% 2.34/2.59 tff(7929,plain,
% 2.34/2.59 (r(s(z), s(s(z))) <=> r(s(z), elem!1)),
% 2.34/2.59 inference(monotonicity,[status(thm)],[7928])).
% 2.34/2.59 tff(7930,plain,
% 2.34/2.59 (r(s(z), elem!1) <=> r(s(z), s(s(z)))),
% 2.34/2.59 inference(symmetry,[status(thm)],[7929])).
% 2.34/2.59 tff(7931,plain,
% 2.34/2.59 (r(s(z), elem!1)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7778, 7896, 95, 6500, 5609, 7301, 7305, 32])).
% 2.34/2.59 tff(7932,plain,
% 2.34/2.59 (r(s(z), s(s(z)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7931, 7930])).
% 2.34/2.59 tff(7933,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6499, 7932])).
% 2.34/2.59 tff(7934,plain,((~r(s(s(s(s(z)))), s(z))) | r(s(z), s(s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7935,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7934, 6499, 95, 5609, 32])).
% 2.34/2.59 tff(7936,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[321, 7935, 255])).
% 2.34/2.59 tff(7937,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5821, 171, 323, 3281, 376, 357, 2527])).
% 2.34/2.59 tff(7938,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7939,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7938, 6500, 6972, 7936, 7311])).
% 2.34/2.59 tff(7940,plain,
% 2.34/2.59 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[454, 7939, 254])).
% 2.34/2.59 tff(7941,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[463, 7940, 61, 7303])).
% 2.34/2.59 tff(7942,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3668, 7941])).
% 2.34/2.59 tff(7943,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7944,plain,
% 2.34/2.59 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7945,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z)))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[7944])).
% 2.34/2.59 tff(7946,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[7945, 7943])).
% 2.34/2.59 tff(7947,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(7948,plain,
% 2.34/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, 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))))), s(z)))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7947, 7946])).
% 2.34/2.59 tff(7949,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7948, 171, 6500, 7290, 7942, 7301, 7305])).
% 2.34/2.59 tff(7950,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[274, 7949])).
% 2.34/2.59 tff(7951,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7952,plain,
% 2.34/2.59 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7953,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[7952])).
% 2.34/2.59 tff(7954,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[7953, 7951])).
% 2.34/2.59 tff(7955,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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))))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(7956,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7955, 7954])).
% 2.34/2.59 tff(7957,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7956, 106, 5609, 61, 7940, 7950])).
% 2.34/2.59 tff(7958,plain,(r(s(z), s(s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | b(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7959,plain,
% 2.34/2.59 (r(s(z), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7958, 6498, 31, 32])).
% 2.34/2.59 tff(7960,plain,
% 2.34/2.59 (b(z, s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6971, 6498, 31, 32])).
% 2.34/2.59 tff(7961,plain,
% 2.34/2.59 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7134, 554, 5609, 126])).
% 2.34/2.59 tff(7962,plain,
% 2.34/2.59 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[205, 7961])).
% 2.34/2.59 tff(7963,plain,
% 2.34/2.59 (~r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5539, 1288, 126, 95])).
% 2.34/2.59 tff(7964,plain,
% 2.34/2.59 (b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[479, 7963])).
% 2.34/2.59 tff(7965,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7966,plain,
% 2.34/2.59 (((~r(s(s(s(s(z)))), s(s(z)))) | (~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(z)))), 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)))))))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(7967,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.34/2.59 inference(monotonicity,[status(thm)],[7966])).
% 2.34/2.59 tff(7968,plain,
% 2.34/2.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.34/2.59 inference(transitivity,[status(thm)],[7967, 7965])).
% 2.34/2.59 tff(7969,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.34/2.59 inference(quant_inst,[status(thm)],[])).
% 2.34/2.59 tff(7970,plain,
% 2.34/2.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.34/2.59 inference(modus_ponens,[status(thm)],[7969, 7968])).
% 2.34/2.59 tff(7971,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7970, 106, 5609, 5567, 1288, 569])).
% 2.34/2.59 tff(7972,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~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)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7973,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7972, 5567, 5609, 1288])).
% 2.34/2.59 tff(7974,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[374, 7973, 355])).
% 2.34/2.59 tff(7975,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[5760, 7974, 7962, 6373])).
% 2.34/2.59 tff(7976,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3668, 7975])).
% 2.34/2.59 tff(7977,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6885, 7976, 126, 5609])).
% 2.34/2.59 tff(7978,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[321, 7977, 255])).
% 2.34/2.59 tff(7979,plain,
% 2.34/2.59 (~r(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6081, 7976, 95, 5567])).
% 2.34/2.59 tff(7980,plain,
% 2.34/2.59 (b(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[454, 7979, 254])).
% 2.34/2.59 tff(7981,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6217, 7980, 7978, 7226, 95, 554, 259, 6371, 3281])).
% 2.34/2.59 tff(7982,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7983,plain,
% 2.34/2.59 (~r(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7982, 1288, 554, 259, 3281, 126, 5609, 95])).
% 2.34/2.59 tff(7984,plain,
% 2.34/2.59 (b(z, s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[293, 7983])).
% 2.34/2.59 tff(7985,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6447, 7984, 7226, 6371, 7964, 7962])).
% 2.34/2.59 tff(7986,plain,
% 2.34/2.59 (r(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[321, 7985, 255])).
% 2.34/2.59 tff(7987,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6885, 7986, 126, 5609])).
% 2.34/2.59 tff(7988,plain,
% 2.34/2.59 (~b(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6375, 1288, 554, 126, 95, 7226])).
% 2.34/2.59 tff(7989,plain,
% 2.34/2.59 (r(z, s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[124, 7988])).
% 2.34/2.59 tff(7990,plain,
% 2.34/2.59 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7189, 7986, 554, 7989, 95, 7984, 6371])).
% 2.34/2.59 tff(7991,plain,
% 2.34/2.59 ($false),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3668, 7990, 7987])).
% 2.34/2.59 tff(7992,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.34/2.59 tff(7993,plain,
% 2.34/2.59 (~r(z, s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7992, 259, 95, 126, 5609, 554, 3281])).
% 2.34/2.59 tff(7994,plain,
% 2.34/2.59 (b(z, s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[498, 7993])).
% 2.34/2.59 tff(7995,plain,
% 2.34/2.59 (~r(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[2952, 600, 554, 95])).
% 2.34/2.59 tff(7996,plain,
% 2.34/2.59 (b(s(s(z)), z)),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[157, 7995])).
% 2.34/2.59 tff(7997,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7244, 600, 3281, 95, 7994, 126, 5609])).
% 2.34/2.59 tff(7998,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[321, 7997, 255])).
% 2.34/2.59 tff(7999,plain,
% 2.34/2.59 (~b(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6217, 7998, 7226, 95, 554, 259, 7996, 3281])).
% 2.34/2.59 tff(8000,plain,
% 2.34/2.59 (r(s(z), s(s(s(s(z)))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[454, 7999, 254])).
% 2.34/2.59 tff(8001,plain,
% 2.34/2.59 (~b(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6937, 7996, 7226, 7962, 7994])).
% 2.34/2.59 tff(8002,plain,
% 2.34/2.59 (r(s(s(s(s(s(z))))), s(z))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[479, 8001])).
% 2.34/2.59 tff(8003,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[6821, 8002, 5609, 8000])).
% 2.34/2.59 tff(8004,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(z)))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[374, 8003, 355])).
% 2.34/2.59 tff(8005,plain,
% 2.34/2.59 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[7068, 8002, 5609, 8000])).
% 2.34/2.59 tff(8006,plain,
% 2.34/2.59 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.34/2.59 inference(unit_resolution,[status(thm)],[3668, 8005])).
% 2.34/2.59 tff(8007,plain,
% 2.34/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(s(z))))), z)))),
% 2.34/2.59 inference(rewrite,[status(thm)],[])).
% 2.34/2.59 tff(8008,plain,
% 2.34/2.59 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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(z)), s(z))) | (~b(z, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8009,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(s(z))))), z))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8008])).
% 2.44/2.60 tff(8010,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(s(z))))), z)))),
% 2.44/2.60 inference(transitivity,[status(thm)],[8009, 8007])).
% 2.44/2.60 tff(8011,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(8012,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[8011, 8010])).
% 2.44/2.60 tff(8013,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8012, 171, 3281, 259, 8006, 7962, 7226, 8004])).
% 2.44/2.60 tff(8014,plain,((~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8015,plain,
% 2.44/2.60 (~r(z, s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8014, 259, 3281, 5609, 95, 554, 126])).
% 2.44/2.60 tff(8016,plain,
% 2.44/2.60 (b(z, s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[124, 8015])).
% 2.44/2.60 tff(8017,plain,
% 2.44/2.60 (~b(s(s(z)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[179, 8016, 7226, 7962])).
% 2.44/2.60 tff(8018,plain,
% 2.44/2.60 (r(s(s(z)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[157, 8017])).
% 2.44/2.60 tff(8019,plain,
% 2.44/2.60 (~r(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5575, 8018, 95, 554])).
% 2.44/2.60 tff(8020,plain,
% 2.44/2.60 (b(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[293, 8019])).
% 2.44/2.60 tff(8021,plain,
% 2.44/2.60 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7147, 8018, 554, 7962, 7994, 95, 126])).
% 2.44/2.60 tff(8022,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[479, 8021])).
% 2.44/2.60 tff(8023,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7124, 8022, 8020, 3281, 554, 5609, 259, 126, 95, 7994])).
% 2.44/2.60 tff(8024,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(s(z), 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), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8025,plain,
% 2.44/2.60 (~b(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8024, 7960, 7959, 6498, 61, 31])).
% 2.44/2.60 tff(8026,plain,
% 2.44/2.60 (r(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[244, 8025])).
% 2.44/2.60 tff(8027,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7224, 6498, 7960, 31, 61])).
% 2.44/2.60 tff(8028,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[145, 8027])).
% 2.44/2.60 tff(8029,plain,
% 2.44/2.60 (~b(s(s(z)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[5918, 8026, 31, 8028, 7959, 61])).
% 2.44/2.60 tff(8030,plain,
% 2.44/2.60 (r(s(s(z)), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[157, 8029])).
% 2.44/2.60 tff(8031,plain,
% 2.44/2.60 (~r(z, s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2952, 8030, 7959, 31])).
% 2.44/2.60 tff(8032,plain,
% 2.44/2.60 (b(z, s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[124, 8031])).
% 2.44/2.60 tff(8033,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7299, 8032, 8026, 31, 61])).
% 2.44/2.60 tff(8034,plain,
% 2.44/2.60 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[7134, 7959, 6498, 61])).
% 2.44/2.60 tff(8035,plain,
% 2.44/2.60 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[205, 8034])).
% 2.44/2.60 tff(8036,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[4802, 8026, 7959, 61])).
% 2.44/2.60 tff(8037,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[225, 8036])).
% 2.44/2.60 tff(8038,plain,
% 2.44/2.60 (~b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6347, 8032, 7960, 8028, 8037, 8035])).
% 2.44/2.60 tff(8039,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[479, 8038, 8033])).
% 2.44/2.60 tff(8040,plain,(b(s(z), s(s(s(s(s(z)))))) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8041,plain,
% 2.44/2.60 (b(s(z), s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8040, 5])).
% 2.44/2.60 tff(8042,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[756, 106, 96, 95, 502, 127])).
% 2.44/2.60 tff(8043,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8044,plain,
% 2.44/2.60 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8043, 127, 95, 96])).
% 2.44/2.60 tff(8045,plain,
% 2.44/2.60 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[479, 8044])).
% 2.44/2.60 tff(8046,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8047,plain,
% 2.44/2.60 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8048,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8047])).
% 2.44/2.60 tff(8049,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[8048, 8046])).
% 2.44/2.60 tff(8050,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(8051,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[8050, 8049])).
% 2.44/2.60 tff(8052,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8051, 171, 83, 1275, 4, 357])).
% 2.44/2.60 tff(8053,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8054,plain,
% 2.44/2.60 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8053, 8045, 1275, 83])).
% 2.44/2.60 tff(8055,plain,
% 2.44/2.60 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[321, 8054, 255])).
% 2.44/2.60 tff(8056,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6875, 8055, 95, 96])).
% 2.44/2.60 tff(8057,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), z)),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[274, 8056])).
% 2.44/2.60 tff(8058,plain,
% 2.44/2.60 (~r(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[281, 106, 96, 95, 8055])).
% 2.44/2.60 tff(8059,plain,
% 2.44/2.60 (b(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[293, 8058])).
% 2.44/2.60 tff(8060,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8061,plain,
% 2.44/2.60 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(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))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8062,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8061])).
% 2.44/2.60 tff(8063,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[8062, 8060])).
% 2.44/2.60 tff(8064,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(8065,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[8064, 8063])).
% 2.44/2.60 tff(8066,plain,
% 2.44/2.60 (~b(z, s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8065, 171, 83, 8059, 8057])).
% 2.44/2.60 tff(8067,plain,
% 2.44/2.60 (r(z, s(s(s(s(s(z))))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[498, 8066])).
% 2.44/2.60 tff(8068,plain,
% 2.44/2.60 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[6149, 263, 95, 2])).
% 2.44/2.60 tff(8069,plain,
% 2.44/2.60 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[374, 8068, 355])).
% 2.44/2.60 tff(8070,plain,
% 2.44/2.60 (~b(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[2535, 8069, 6877, 158])).
% 2.44/2.60 tff(8071,plain,
% 2.44/2.60 (r(z, s(s(s(s(z)))))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[293, 8070])).
% 2.44/2.60 tff(8072,plain,
% 2.44/2.60 ($false),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[281, 106, 96, 95, 8071, 263])).
% 2.44/2.60 tff(8073,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.60 tff(8074,plain,
% 2.44/2.60 (~r(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8073, 8055, 95, 96])).
% 2.44/2.60 tff(8075,plain,
% 2.44/2.60 (b(s(s(z)), s(z))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[244, 8074])).
% 2.44/2.60 tff(8076,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8077,plain,
% 2.44/2.60 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8078,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8077])).
% 2.44/2.60 tff(8079,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[8078, 8076])).
% 2.44/2.60 tff(8080,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.60 inference(quant_inst,[status(thm)],[])).
% 2.44/2.60 tff(8081,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.60 inference(modus_ponens,[status(thm)],[8080, 8079])).
% 2.44/2.60 tff(8082,plain,
% 2.44/2.60 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[8081, 171, 8075, 1275, 8045])).
% 2.44/2.60 tff(8083,plain,
% 2.44/2.60 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.60 inference(unit_resolution,[status(thm)],[225, 8082])).
% 2.44/2.60 tff(8084,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8085,plain,
% 2.44/2.60 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(rewrite,[status(thm)],[])).
% 2.44/2.60 tff(8086,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.60 inference(monotonicity,[status(thm)],[8085])).
% 2.44/2.60 tff(8087,plain,
% 2.44/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.60 inference(transitivity,[status(thm)],[8086, 8084])).
% 2.44/2.60 tff(8088,plain,
% 2.44/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8089,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8088, 8087])).
% 2.44/2.61 tff(8090,plain,
% 2.44/2.61 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8089, 171, 259, 83, 1275, 4])).
% 2.44/2.61 tff(8091,plain,
% 2.44/2.61 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[205, 8090])).
% 2.44/2.61 tff(8092,plain,
% 2.44/2.61 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8081, 171, 259, 1275, 4])).
% 2.44/2.61 tff(8093,plain,
% 2.44/2.61 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[225, 8092])).
% 2.44/2.61 tff(8094,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8095,plain,
% 2.44/2.61 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8096,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8095])).
% 2.44/2.61 tff(8097,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8096, 8094])).
% 2.44/2.61 tff(8098,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8099,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8098, 8097])).
% 2.44/2.61 tff(8100,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8099, 106, 600, 8093, 127, 8091])).
% 2.44/2.61 tff(8101,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(8102,plain,
% 2.44/2.61 (~b(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8101, 600, 127, 1275, 8045, 83])).
% 2.44/2.61 tff(8103,plain,
% 2.44/2.61 (r(s(s(z)), s(z))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[244, 8102])).
% 2.44/2.61 tff(8104,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[112, 106, 96, 8103, 95, 600])).
% 2.44/2.61 tff(8105,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(8106,plain,
% 2.44/2.61 (~r(z, s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8105, 127, 95, 96, 1275, 83])).
% 2.44/2.61 tff(8107,plain,
% 2.44/2.61 (b(z, s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[124, 8106])).
% 2.44/2.61 tff(8108,plain,
% 2.44/2.61 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8089, 171, 8075, 83, 1275, 8045])).
% 2.44/2.61 tff(8109,plain,
% 2.44/2.61 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[205, 8108])).
% 2.44/2.61 tff(8110,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8111,plain,
% 2.44/2.61 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8112,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8111])).
% 2.44/2.61 tff(8113,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8112, 8110])).
% 2.44/2.61 tff(8114,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8115,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8114, 8113])).
% 2.44/2.61 tff(8116,plain,
% 2.44/2.61 (~r(z, s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8115, 106, 260, 396, 1288])).
% 2.44/2.61 tff(8117,plain,
% 2.44/2.61 (b(z, s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[293, 8116])).
% 2.44/2.61 tff(8118,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8119,plain,
% 2.44/2.61 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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(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(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8120,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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(s(z))))), s(s(z))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8119])).
% 2.44/2.61 tff(8121,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8120, 8118])).
% 2.44/2.61 tff(8122,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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)))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8123,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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(s(z))))), s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8122, 8121])).
% 2.44/2.61 tff(8124,plain,
% 2.44/2.61 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8123, 106, 260, 396, 501])).
% 2.44/2.61 tff(8125,plain,
% 2.44/2.61 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[374, 8124, 355])).
% 2.44/2.61 tff(8126,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8127,plain,
% 2.44/2.61 (((~r(s(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(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8128,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8127])).
% 2.44/2.61 tff(8129,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8128, 8126])).
% 2.44/2.61 tff(8130,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8131,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8130, 8129])).
% 2.44/2.61 tff(8132,plain,
% 2.44/2.61 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8131, 106, 260, 396, 501])).
% 2.44/2.61 tff(8133,plain,
% 2.44/2.61 (b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[351, 8132])).
% 2.44/2.61 tff(8134,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[5981, 8133, 8125, 161, 8117])).
% 2.44/2.61 tff(8135,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(8136,plain,
% 2.44/2.61 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8135, 8067, 8083, 8109, 8107])).
% 2.44/2.61 tff(8137,plain,
% 2.44/2.61 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[3668, 8136])).
% 2.44/2.61 tff(8138,plain,
% 2.44/2.61 (~r(s(s(z)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[959, 8083, 96, 127])).
% 2.44/2.61 tff(8139,plain,
% 2.44/2.61 (b(s(s(z)), z)),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[157, 8138])).
% 2.44/2.61 tff(8140,plain,
% 2.44/2.61 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[6307, 8139, 8107, 8075, 8057])).
% 2.44/2.61 tff(8141,plain,
% 2.44/2.61 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[374, 8140, 355])).
% 2.44/2.61 tff(8142,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8143,plain,
% 2.44/2.61 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8144,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8143])).
% 2.44/2.61 tff(8145,plain,
% 2.44/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8144, 8142])).
% 2.44/2.61 tff(8146,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8147,plain,
% 2.44/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8146, 8145])).
% 2.44/2.61 tff(8148,plain,
% 2.44/2.61 ($false),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8147, 106, 554, 263, 569, 501])).
% 2.44/2.61 tff(8149,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.61 tff(8150,plain,
% 2.44/2.61 (~r(s(z), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8149, 8141, 8109, 8055])).
% 2.44/2.61 tff(8151,plain,
% 2.44/2.61 (b(s(z), s(s(z)))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[550, 8150])).
% 2.44/2.61 tff(8152,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8153,plain,
% 2.44/2.61 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.61 inference(rewrite,[status(thm)],[])).
% 2.44/2.61 tff(8154,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.61 inference(monotonicity,[status(thm)],[8153])).
% 2.44/2.61 tff(8155,plain,
% 2.44/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.61 inference(transitivity,[status(thm)],[8154, 8152])).
% 2.44/2.61 tff(8156,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.61 inference(quant_inst,[status(thm)],[])).
% 2.44/2.61 tff(8157,plain,
% 2.44/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.61 inference(modus_ponens,[status(thm)],[8156, 8155])).
% 2.44/2.61 tff(8158,plain,
% 2.44/2.61 (~b(s(z), s(s(s(s(z)))))),
% 2.44/2.61 inference(unit_resolution,[status(thm)],[8157, 171, 8151, 8107, 83, 8045, 8057])).
% 2.44/2.62 tff(8159,plain,
% 2.44/2.62 (r(s(z), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[454, 8158, 254])).
% 2.44/2.62 tff(8160,plain,
% 2.44/2.62 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[4223, 171, 3686, 83, 838])).
% 2.44/2.62 tff(8161,plain,
% 2.44/2.62 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2842, 8160, 2264])).
% 2.44/2.62 tff(8162,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8163,plain,
% 2.44/2.62 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8164,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8163])).
% 2.44/2.62 tff(8165,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[8164, 8162])).
% 2.44/2.62 tff(8166,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8167,plain,
% 2.44/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8166, 8165])).
% 2.44/2.62 tff(8168,plain,
% 2.44/2.62 (~b(s(z), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8167, 171, 3686, 83, 838, 1275])).
% 2.44/2.62 tff(8169,plain,
% 2.44/2.62 (r(s(z), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[1996, 8168])).
% 2.44/2.62 tff(8170,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8171,plain,
% 2.44/2.62 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8172,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8171])).
% 2.44/2.62 tff(8173,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[8172, 8170])).
% 2.44/2.62 tff(8174,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8175,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8174, 8173])).
% 2.44/2.62 tff(8176,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8175, 106, 1998, 3, 263, 2828])).
% 2.44/2.62 tff(8177,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8178,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8177, 8169, 8161, 3, 263])).
% 2.44/2.62 tff(8179,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8180,plain,
% 2.44/2.62 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8179, 8159, 8055, 8137, 83, 1275])).
% 2.44/2.62 tff(8181,plain,
% 2.44/2.62 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2614, 8180])).
% 2.44/2.62 tff(8182,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8183,plain,
% 2.44/2.62 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8184,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8183])).
% 2.44/2.62 tff(8185,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.44/2.62 inference(transitivity,[status(thm)],[8184, 8182])).
% 2.44/2.62 tff(8186,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~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)))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8187,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8186, 8185])).
% 2.44/2.62 tff(8188,plain,
% 2.44/2.62 (~r(s(s(s(z))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8187, 106, 8181, 8083, 8067])).
% 2.44/2.62 tff(8189,plain,
% 2.44/2.62 (b(s(s(s(z))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[953, 25, 194, 8188])).
% 2.44/2.62 tff(8190,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(z)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[987, 106, 8181, 8083, 8109])).
% 2.44/2.62 tff(8191,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(z)))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2642, 8190])).
% 2.44/2.62 tff(8192,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2635, 171, 8075, 8107, 8139, 8191, 8189])).
% 2.44/2.62 tff(8193,plain,((~r(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8194,plain,
% 2.44/2.62 (~r(s(s(s(s(s(z))))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8193, 83, 1275, 96, 95])).
% 2.44/2.62 tff(8195,plain,
% 2.44/2.62 (b(s(s(s(s(s(z))))), z)),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[145, 8194])).
% 2.44/2.62 tff(8196,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8197,plain,
% 2.44/2.62 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8198,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8197])).
% 2.44/2.62 tff(8199,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[8198, 8196])).
% 2.44/2.62 tff(8200,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8201,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 2.44/2.62 tff(8202,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8201, 106, 260, 502, 3, 263])).
% 2.44/2.62 tff(8203,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8204,plain,
% 2.44/2.62 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8203, 263, 3, 502])).
% 2.44/2.62 tff(8205,plain,
% 2.44/2.62 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[3668, 8204])).
% 2.44/2.62 tff(8206,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8207,plain,
% 2.44/2.62 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8208,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8207])).
% 2.44/2.62 tff(8209,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.62 inference(transitivity,[status(thm)],[8208, 8206])).
% 2.44/2.62 tff(8210,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8211,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8210, 8209])).
% 2.44/2.62 tff(8212,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8211, 106, 1357, 502, 3, 747])).
% 2.44/2.62 tff(8213,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8214,plain,
% 2.44/2.62 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8213, 747, 3, 502])).
% 2.44/2.62 tff(8215,plain,
% 2.44/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8216,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(quant_inst,[status(thm)],[])).
% 2.44/2.62 tff(8217,plain,
% 2.44/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.62 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 2.44/2.62 tff(8218,plain,
% 2.44/2.62 ($false),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8217, 106, 2604, 502, 3, 747])).
% 2.44/2.62 tff(8219,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.62 tff(8220,plain,
% 2.44/2.62 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[8219, 3, 502, 747])).
% 2.44/2.62 tff(8221,plain,
% 2.44/2.62 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.62 inference(unit_resolution,[status(thm)],[2614, 8220])).
% 2.44/2.62 tff(8222,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8223,plain,
% 2.44/2.62 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.62 inference(rewrite,[status(thm)],[])).
% 2.44/2.62 tff(8224,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.62 inference(monotonicity,[status(thm)],[8223])).
% 2.44/2.62 tff(8225,plain,
% 2.44/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8224, 8222])).
% 2.44/2.63 tff(8226,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8227,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8226, 8225])).
% 2.44/2.63 tff(8228,plain,
% 2.44/2.63 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8227, 171, 3686, 8221, 1384])).
% 2.44/2.63 tff(8229,plain,
% 2.44/2.63 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2842, 8228, 2839])).
% 2.44/2.63 tff(8230,plain,
% 2.44/2.63 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4229, 2839])).
% 2.44/2.63 tff(8231,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8232,plain,
% 2.44/2.63 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8233,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[8232])).
% 2.44/2.63 tff(8234,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8233, 8231])).
% 2.44/2.63 tff(8235,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8236,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8235, 8234])).
% 2.44/2.63 tff(8237,plain,
% 2.44/2.63 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8236, 171, 3686, 8221, 1384])).
% 2.44/2.63 tff(8238,plain,
% 2.44/2.63 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4240, 25, 8237, 8230])).
% 2.44/2.63 tff(8239,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8240,plain,
% 2.44/2.63 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8241,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[8240])).
% 2.44/2.63 tff(8242,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8241, 8239])).
% 2.44/2.63 tff(8243,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8244,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8243, 8242])).
% 2.44/2.63 tff(8245,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8244, 106, 3, 8238, 747, 8229])).
% 2.44/2.63 tff(8246,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(8247,plain,
% 2.44/2.63 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8246, 747, 2264, 3, 3686, 502])).
% 2.44/2.63 tff(8248,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1368, 8247, 8214])).
% 2.44/2.63 tff(8249,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(8250,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8249, 8205, 3, 502])).
% 2.44/2.63 tff(8251,plain,
% 2.44/2.63 (b(s(s(s(z))), s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1173, 8250])).
% 2.44/2.63 tff(8252,plain,
% 2.44/2.63 (~r(z, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[4309, 8205, 83, 159, 3, 263])).
% 2.44/2.63 tff(8253,plain,
% 2.44/2.63 (b(z, s(z))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[93, 8252])).
% 2.44/2.63 tff(8254,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8255,plain,
% 2.44/2.63 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8256,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[8255])).
% 2.44/2.63 tff(8257,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8256, 8254])).
% 2.44/2.63 tff(8258,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8259,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8258, 8257])).
% 2.44/2.63 tff(8260,plain,
% 2.44/2.63 (~b(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8259, 171, 3281, 1188, 1976])).
% 2.44/2.63 tff(8261,plain,
% 2.44/2.63 (r(s(s(s(z))), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[953, 25, 194, 8260])).
% 2.44/2.63 tff(8262,plain,
% 2.44/2.63 (~b(s(s(s(z))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[5518, 1976, 259, 1188])).
% 2.44/2.63 tff(8263,plain,
% 2.44/2.63 (r(s(s(s(z))), s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2640, 25, 8262, 80])).
% 2.44/2.63 tff(8264,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8265,plain,
% 2.44/2.63 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8266,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[8265])).
% 2.44/2.63 tff(8267,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8266, 8264])).
% 2.44/2.63 tff(8268,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8269,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8268, 8267])).
% 2.44/2.63 tff(8270,plain,
% 2.44/2.63 (~b(z, s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8269, 171, 3281, 259, 1188, 1976])).
% 2.44/2.63 tff(8271,plain,
% 2.44/2.63 (r(z, s(s(z)))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[124, 8270])).
% 2.44/2.63 tff(8272,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8273,plain,
% 2.44/2.63 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8274,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.44/2.63 inference(monotonicity,[status(thm)],[8273])).
% 2.44/2.63 tff(8275,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.63 inference(transitivity,[status(thm)],[8274, 8272])).
% 2.44/2.63 tff(8276,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8277,plain,
% 2.44/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8276, 8275])).
% 2.44/2.63 tff(8278,plain,
% 2.44/2.63 (~b(s(s(z)), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8277, 171, 3281, 259, 1188, 1976])).
% 2.44/2.63 tff(8279,plain,
% 2.44/2.63 (r(s(s(z)), z)),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[157, 8278])).
% 2.44/2.63 tff(8280,plain,
% 2.44/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8281,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.44/2.63 inference(quant_inst,[status(thm)],[])).
% 2.44/2.63 tff(8282,plain,
% 2.44/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 2.44/2.63 inference(modus_ponens,[status(thm)],[8281, 8280])).
% 2.44/2.63 tff(8283,plain,
% 2.44/2.63 ($false),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8282, 106, 8279, 8271, 8263, 8261])).
% 2.44/2.63 tff(8284,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.63 tff(8285,plain,
% 2.44/2.63 (~b(s(z), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8284, 8253, 259, 8251])).
% 2.44/2.63 tff(8286,plain,
% 2.44/2.63 (r(s(z), s(s(s(z))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[1996, 8285])).
% 2.44/2.63 tff(8287,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8177, 8286, 3, 263])).
% 2.44/2.63 tff(8288,plain,
% 2.44/2.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2842, 8287, 2264])).
% 2.44/2.63 tff(8289,plain,
% 2.44/2.63 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[8177, 1998, 3, 263])).
% 2.44/2.63 tff(8290,plain,
% 2.44/2.63 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.63 inference(unit_resolution,[status(thm)],[2842, 8289, 2264])).
% 2.44/2.63 tff(8291,plain,
% 2.44/2.63 (((~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(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.63 inference(rewrite,[status(thm)],[])).
% 2.44/2.63 tff(8292,plain,
% 2.44/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8291])).
% 2.44/2.64 tff(8293,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8292, 4218])).
% 2.44/2.64 tff(8294,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(8295,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[8294, 8293])).
% 2.44/2.64 tff(8296,plain,
% 2.44/2.64 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8295, 171, 8205, 83, 8290])).
% 2.44/2.64 tff(8297,plain,
% 2.44/2.64 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2614, 8296])).
% 2.44/2.64 tff(8298,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8299,plain,
% 2.44/2.64 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8300,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8299])).
% 2.44/2.64 tff(8301,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8300, 8298])).
% 2.44/2.64 tff(8302,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(8303,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[8302, 8301])).
% 2.44/2.64 tff(8304,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8303, 106, 8297, 1357, 502, 1998])).
% 2.44/2.64 tff(8305,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(8306,plain,
% 2.44/2.64 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8305, 8286, 502, 83, 3, 263])).
% 2.44/2.64 tff(8307,plain,
% 2.44/2.64 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[1368, 8306])).
% 2.44/2.64 tff(8308,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8309,plain,
% 2.44/2.64 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8310,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8309])).
% 2.44/2.64 tff(8311,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8310, 8308])).
% 2.44/2.64 tff(8312,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(8313,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[8312, 8311])).
% 2.44/2.64 tff(8314,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8313, 171, 3686, 1188, 83, 1275, 1384, 6462])).
% 2.44/2.64 tff(8315,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(8316,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8315, 8205, 8251, 83, 1275, 8307])).
% 2.44/2.64 tff(8317,plain,
% 2.44/2.64 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4240, 25, 8316, 4230])).
% 2.44/2.64 tff(8318,plain,
% 2.44/2.64 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[6485, 8317, 8286, 263])).
% 2.44/2.64 tff(8319,plain,
% 2.44/2.64 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2614, 8318])).
% 2.44/2.64 tff(8320,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[4223, 171, 8205, 83, 8319, 8288])).
% 2.44/2.64 tff(8321,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(8322,plain,
% 2.44/2.64 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8321, 259, 1275, 502, 3, 83, 159])).
% 2.44/2.64 tff(8323,plain,
% 2.44/2.64 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[321, 8322, 255])).
% 2.44/2.64 tff(8324,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8325,plain,
% 2.44/2.64 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8326,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8325])).
% 2.44/2.64 tff(8327,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8326, 8324])).
% 2.44/2.64 tff(8328,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(8329,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[8328, 8327])).
% 2.44/2.64 tff(8330,plain,
% 2.44/2.64 ($false),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8329, 171, 3686, 83, 1275, 357])).
% 2.44/2.64 tff(8331,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.64 tff(8332,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8331, 8323, 1275, 83])).
% 2.44/2.64 tff(8333,plain,
% 2.44/2.64 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3668, 8332])).
% 2.44/2.64 tff(8334,plain,
% 2.44/2.64 (~r(z, s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[2497, 106, 96, 502, 3])).
% 2.44/2.64 tff(8335,plain,
% 2.44/2.64 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[496, 25, 8334])).
% 2.44/2.64 tff(8336,plain,
% 2.44/2.64 (b(z, s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8335, 6021])).
% 2.44/2.64 tff(8337,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8338,plain,
% 2.44/2.64 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8339,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8338])).
% 2.44/2.64 tff(8340,plain,
% 2.44/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8339, 8337])).
% 2.44/2.64 tff(8341,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.64 inference(quant_inst,[status(thm)],[])).
% 2.44/2.64 tff(8342,plain,
% 2.44/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.64 inference(modus_ponens,[status(thm)],[8341, 8340])).
% 2.44/2.64 tff(8343,plain,
% 2.44/2.64 (~b(z, s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8342, 171, 83, 1275, 159, 357, 8336])).
% 2.44/2.64 tff(8344,plain,
% 2.44/2.64 (r(z, s(s(s(s(z)))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[291, 25, 8343, 286])).
% 2.44/2.64 tff(8345,plain,
% 2.44/2.64 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[8331, 357, 1275, 83])).
% 2.44/2.64 tff(8346,plain,
% 2.44/2.64 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.64 inference(unit_resolution,[status(thm)],[3668, 8345])).
% 2.44/2.64 tff(8347,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8348,plain,
% 2.44/2.64 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(rewrite,[status(thm)],[])).
% 2.44/2.64 tff(8349,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.44/2.64 inference(monotonicity,[status(thm)],[8348])).
% 2.44/2.64 tff(8350,plain,
% 2.44/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.44/2.64 inference(transitivity,[status(thm)],[8349, 8347])).
% 2.44/2.64 tff(8351,plain,
% 2.44/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(z))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8352,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8351, 8350])).
% 2.44/2.65 tff(8353,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8352, 106, 96, 8346, 8344, 3])).
% 2.44/2.65 tff(8354,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(8355,plain,
% 2.44/2.65 (~r(z, s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8354, 8323, 83, 1275, 159, 3, 502])).
% 2.44/2.65 tff(8356,plain,
% 2.44/2.65 (b(z, s(z))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[93, 8355])).
% 2.44/2.65 tff(8357,plain,
% 2.44/2.65 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 2.44/2.65 inference(symmetry,[status(thm)],[914])).
% 2.44/2.65 tff(8358,plain,
% 2.44/2.65 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8357])).
% 2.44/2.65 tff(8359,plain,
% 2.44/2.65 (~(z = s(s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[194, 8358])).
% 2.44/2.65 tff(8360,plain,
% 2.44/2.65 (~b(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8284, 3281, 259, 1188])).
% 2.44/2.65 tff(8361,plain,
% 2.44/2.65 (r(s(z), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[1996, 8360])).
% 2.44/2.65 tff(8362,plain,
% 2.44/2.65 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2836, 8361, 8333, 3])).
% 2.44/2.65 tff(8363,plain,
% 2.44/2.65 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2842, 8362, 2264])).
% 2.44/2.65 tff(8364,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8365,plain,
% 2.44/2.65 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8366,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8365])).
% 2.44/2.65 tff(8367,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[8366, 8364])).
% 2.44/2.65 tff(8368,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8369,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8368, 8367])).
% 2.44/2.65 tff(8370,plain,
% 2.44/2.65 (~b(z, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8369, 171, 3281, 1188, 83, 1275, 8363])).
% 2.44/2.65 tff(8371,plain,
% 2.44/2.65 (((~![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)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8372,plain,
% 2.44/2.65 ((~![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)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8373,plain,
% 2.44/2.65 ((~![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))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8372, 8371])).
% 2.44/2.65 tff(8374,plain,
% 2.44/2.65 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8373, 25, 8370])).
% 2.44/2.65 tff(8375,plain,
% 2.44/2.65 (r(z, s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8374, 8359])).
% 2.44/2.65 tff(8376,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8377,plain,
% 2.44/2.65 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8378,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8377])).
% 2.44/2.65 tff(8379,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.65 inference(transitivity,[status(thm)],[8378, 8376])).
% 2.44/2.65 tff(8380,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8381,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8380, 8379])).
% 2.44/2.65 tff(8382,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8381, 171, 3281, 3133, 1275, 159])).
% 2.44/2.65 tff(8383,plain,((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(8384,plain,
% 2.44/2.65 (~b(s(z), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8383, 3281, 159, 1275])).
% 2.44/2.65 tff(8385,plain,
% 2.44/2.65 (r(s(z), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[30, 8384])).
% 2.44/2.65 tff(8386,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8387,plain,
% 2.44/2.65 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8388,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8387])).
% 2.44/2.65 tff(8389,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[8388, 8386])).
% 2.44/2.65 tff(8390,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8391,plain,
% 2.44/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8390, 8389])).
% 2.44/2.65 tff(8392,plain,
% 2.44/2.65 (~b(s(s(z)), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8391, 171, 259, 1188, 83, 1275, 8363])).
% 2.44/2.65 tff(8393,plain,
% 2.44/2.65 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[979, 25, 8392])).
% 2.44/2.65 tff(8394,plain,
% 2.44/2.65 (r(s(s(z)), s(s(s(z))))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8393, 900])).
% 2.44/2.65 tff(8395,plain,
% 2.44/2.65 (~b(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[6237, 1, 259, 3281])).
% 2.44/2.65 tff(8396,plain,
% 2.44/2.65 (r(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[550, 8395])).
% 2.44/2.65 tff(8397,plain,
% 2.44/2.65 (~r(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[2686, 8396, 95, 2678])).
% 2.44/2.65 tff(8398,plain,
% 2.44/2.65 (b(z, s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[124, 8397])).
% 2.44/2.65 tff(8399,plain,
% 2.44/2.65 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[215, 8398, 1, 159])).
% 2.44/2.65 tff(8400,plain,
% 2.44/2.65 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[225, 8399])).
% 2.44/2.65 tff(8401,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8402,plain,
% 2.44/2.65 (((~r(s(s(z)), s(s(s(z))))) | (~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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8403,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8402])).
% 2.44/2.65 tff(8404,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[8403, 8401])).
% 2.44/2.65 tff(8405,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~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))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8406,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8405, 8404])).
% 2.44/2.65 tff(8407,plain,
% 2.44/2.65 ($false),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8406, 106, 8396, 502, 8400, 2678])).
% 2.44/2.65 tff(8408,plain,((~b(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.65 tff(8409,plain,
% 2.44/2.65 (~b(s(s(z)), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8408, 8394, 502, 159, 8385, 259, 3281])).
% 2.44/2.65 tff(8410,plain,
% 2.44/2.65 (r(s(s(z)), z)),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[157, 8409])).
% 2.44/2.65 tff(8411,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8412,plain,
% 2.44/2.65 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8413,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z)))))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8412])).
% 2.44/2.65 tff(8414,plain,
% 2.44/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))))),
% 2.44/2.65 inference(transitivity,[status(thm)],[8413, 8411])).
% 2.44/2.65 tff(8415,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.44/2.65 inference(quant_inst,[status(thm)],[])).
% 2.44/2.65 tff(8416,plain,
% 2.44/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z)))))),
% 2.44/2.65 inference(modus_ponens,[status(thm)],[8415, 8414])).
% 2.44/2.65 tff(8417,plain,
% 2.44/2.65 (~r(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[8416, 106, 8410, 8385, 8375])).
% 2.44/2.65 tff(8418,plain,
% 2.44/2.65 (b(s(z), s(s(z)))),
% 2.44/2.65 inference(unit_resolution,[status(thm)],[550, 8417])).
% 2.44/2.65 tff(8419,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8420,plain,
% 2.44/2.65 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.65 inference(rewrite,[status(thm)],[])).
% 2.44/2.65 tff(8421,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.44/2.65 inference(monotonicity,[status(thm)],[8420])).
% 2.44/2.65 tff(8422,plain,
% 2.44/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8421, 8419])).
% 2.44/2.66 tff(8423,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(8424,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 2.44/2.66 tff(8425,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8424, 171, 8418, 3281, 259, 8323])).
% 2.44/2.66 tff(8426,plain,
% 2.44/2.66 (~b(z, s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6227, 171, 8418, 3281, 259])).
% 2.44/2.66 tff(8427,plain,
% 2.44/2.66 (r(z, s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[124, 8426])).
% 2.44/2.66 tff(8428,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[363, 171, 8418, 259, 8323])).
% 2.44/2.66 tff(8429,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[374, 8428, 355])).
% 2.44/2.66 tff(8430,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3707, 8429, 8427, 8410])).
% 2.44/2.66 tff(8431,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[272, 25, 52, 8430, 8425])).
% 2.44/2.66 tff(8432,plain,((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(8433,plain,
% 2.44/2.66 (~b(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8432, 8356, 502, 159, 259, 83, 1275, 3])).
% 2.44/2.66 tff(8434,plain,
% 2.44/2.66 (r(s(s(s(z))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1173, 8433])).
% 2.44/2.66 tff(8435,plain,
% 2.44/2.66 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8219, 8434, 3, 502])).
% 2.44/2.66 tff(8436,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2614, 8435])).
% 2.44/2.66 tff(8437,plain,
% 2.44/2.66 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8213, 8434, 3, 502])).
% 2.44/2.66 tff(8438,plain,
% 2.44/2.66 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1368, 8437])).
% 2.44/2.66 tff(8439,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8440,plain,
% 2.44/2.66 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8441,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8440])).
% 2.44/2.66 tff(8442,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8441, 8439])).
% 2.44/2.66 tff(8443,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(8444,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[8443, 8442])).
% 2.44/2.66 tff(8445,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8444, 171, 1976, 838, 1275, 1384])).
% 2.44/2.66 tff(8446,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(8447,plain,
% 2.44/2.66 (~b(s(z), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8446, 8438, 1275, 8436])).
% 2.44/2.66 tff(8448,plain,
% 2.44/2.66 (r(s(z), s(s(s(z))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[1996, 8447])).
% 2.44/2.66 tff(8449,plain,
% 2.44/2.66 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2836, 8448, 8333, 3])).
% 2.44/2.66 tff(8450,plain,
% 2.44/2.66 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[2842, 8449, 2264])).
% 2.44/2.66 tff(8451,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8452,plain,
% 2.44/2.66 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8453,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8452])).
% 2.44/2.66 tff(8454,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8453, 8451])).
% 2.44/2.66 tff(8455,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(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(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(8456,plain,
% 2.44/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[8455, 8454])).
% 2.44/2.66 tff(8457,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8456, 171, 83, 8436, 1275, 8438, 8450, 8323])).
% 2.44/2.66 tff(8458,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(8459,plain,
% 2.44/2.66 (~b(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8458, 83, 1275, 3, 502, 159])).
% 2.44/2.66 tff(8460,plain,
% 2.44/2.66 (r(s(s(z)), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[244, 8459])).
% 2.44/2.66 tff(8461,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(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(z)))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8462,plain,
% 2.44/2.66 (((~r(s(z), s(s(s(s(z)))))) | (~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))))) <=> ((~r(s(s(z)), s(z))) | (~r(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(z)))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8463,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8462])).
% 2.44/2.66 tff(8464,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(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(z)))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8463, 8461])).
% 2.44/2.66 tff(8465,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(8466,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[8465, 8464])).
% 2.44/2.66 tff(8467,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8466, 106, 2, 502, 3, 396])).
% 2.44/2.66 tff(8468,plain,((~r(s(z), s(s(s(s(z)))))) | (~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))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(8469,plain,
% 2.44/2.66 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8468, 8460, 3, 502])).
% 2.44/2.66 tff(8470,plain,
% 2.44/2.66 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[225, 8469])).
% 2.44/2.66 tff(8471,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(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(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8472,plain,
% 2.44/2.66 (((~r(s(z), s(s(s(s(z)))))) | (~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)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(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(z))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8473,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z)))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8472])).
% 2.44/2.66 tff(8474,plain,
% 2.44/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(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(z))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8473, 8471])).
% 2.44/2.66 tff(8475,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(quant_inst,[status(thm)],[])).
% 2.44/2.66 tff(8476,plain,
% 2.44/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.66 inference(modus_ponens,[status(thm)],[8475, 8474])).
% 2.44/2.66 tff(8477,plain,
% 2.44/2.66 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8476, 106, 8460, 502, 3])).
% 2.44/2.66 tff(8478,plain,
% 2.44/2.66 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[203, 25, 8477, 198])).
% 2.44/2.66 tff(8479,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8331, 3686, 1275, 83])).
% 2.44/2.66 tff(8480,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[321, 8479, 255])).
% 2.44/2.66 tff(8481,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[374, 5783, 355])).
% 2.44/2.66 tff(8482,plain,
% 2.44/2.66 ($false),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[6011, 8481, 8480, 3, 2])).
% 2.44/2.66 tff(8483,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.66 tff(8484,plain,
% 2.44/2.66 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8483, 8460, 3, 8470, 8478, 1275, 83])).
% 2.44/2.66 tff(8485,plain,
% 2.44/2.66 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[3668, 8484])).
% 2.44/2.66 tff(8486,plain,
% 2.44/2.66 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8203, 8485, 3, 502])).
% 2.44/2.66 tff(8487,plain,
% 2.44/2.66 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[321, 8486, 255])).
% 2.44/2.66 tff(8488,plain,
% 2.44/2.66 (~r(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8354, 8487, 83, 1275, 159, 3, 502])).
% 2.44/2.66 tff(8489,plain,
% 2.44/2.66 (b(z, s(z))),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[93, 8488])).
% 2.44/2.66 tff(8490,plain,
% 2.44/2.66 (~b(s(z), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[8383, 8489, 159, 1275])).
% 2.44/2.66 tff(8491,plain,
% 2.44/2.66 (r(s(z), z)),
% 2.44/2.66 inference(unit_resolution,[status(thm)],[30, 8490])).
% 2.44/2.66 tff(8492,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8493,plain,
% 2.44/2.66 (((~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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(rewrite,[status(thm)],[])).
% 2.44/2.66 tff(8494,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.44/2.66 inference(monotonicity,[status(thm)],[8493])).
% 2.44/2.66 tff(8495,plain,
% 2.44/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.44/2.66 inference(transitivity,[status(thm)],[8494, 8492])).
% 2.44/2.67 tff(8496,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8497,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8496, 8495])).
% 2.44/2.67 tff(8498,plain,
% 2.44/2.67 (~b(s(z), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8497, 171, 1275, 8478, 8470])).
% 2.44/2.67 tff(8499,plain,
% 2.44/2.67 (r(s(z), s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[550, 8498])).
% 2.44/2.67 tff(8500,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), z)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8501,plain,
% 2.44/2.67 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, 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(z))) | (~b(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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8502,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), z))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8501])).
% 2.44/2.67 tff(8503,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), z)))),
% 2.44/2.67 inference(transitivity,[status(thm)],[8502, 8500])).
% 2.44/2.67 tff(8504,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, 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)))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8505,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8504, 8503])).
% 2.44/2.67 tff(8506,plain,
% 2.44/2.67 (~b(s(s(z)), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8505, 171, 8489, 1275, 8478, 8470, 159])).
% 2.44/2.67 tff(8507,plain,
% 2.44/2.67 (r(s(s(z)), z)),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[157, 8506])).
% 2.44/2.67 tff(8508,plain,
% 2.44/2.67 (~r(z, s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2952, 8507, 8499, 8491])).
% 2.44/2.67 tff(8509,plain,
% 2.44/2.67 (b(z, s(s(z)))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[124, 8508])).
% 2.44/2.67 tff(8510,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3465, 171, 8509, 8478, 8470, 159])).
% 2.44/2.67 tff(8511,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(8512,plain,
% 2.44/2.67 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8511, 502, 1275, 83, 8195])).
% 2.44/2.67 tff(8513,plain,
% 2.44/2.67 (b(s(z), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[454, 8512, 254])).
% 2.44/2.67 tff(8514,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8515,plain,
% 2.44/2.67 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8516,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8515])).
% 2.44/2.67 tff(8517,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[8516, 8514])).
% 2.44/2.67 tff(8518,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8519,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8518, 8517])).
% 2.44/2.67 tff(8520,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8519, 171, 3686, 83, 1275, 376])).
% 2.44/2.67 tff(8521,plain,((~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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(8522,plain,
% 2.44/2.67 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8521, 8513, 1275, 83])).
% 2.44/2.67 tff(8523,plain,
% 2.44/2.67 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[3668, 8522])).
% 2.44/2.67 tff(8524,plain,
% 2.44/2.67 (~r(z, s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[486, 106, 96, 95, 502])).
% 2.44/2.67 tff(8525,plain,
% 2.44/2.67 (b(z, s(s(s(s(s(z))))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[498, 8524])).
% 2.44/2.67 tff(8526,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[5552, 8523, 502, 95])).
% 2.44/2.67 tff(8527,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[321, 8526, 255])).
% 2.44/2.67 tff(8528,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8529,plain,
% 2.44/2.67 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8530,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8529])).
% 2.44/2.67 tff(8531,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[8530, 8528])).
% 2.44/2.67 tff(8532,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8533,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8532, 8531])).
% 2.44/2.67 tff(8534,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8533, 106, 260, 2604, 502, 2828])).
% 2.44/2.67 tff(8535,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(8536,plain,
% 2.44/2.67 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8535, 2604, 502, 260])).
% 2.44/2.67 tff(8537,plain,
% 2.44/2.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2842, 8536, 2264])).
% 2.44/2.67 tff(8538,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8539,plain,
% 2.44/2.67 (((~b(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(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8540,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8539])).
% 2.44/2.67 tff(8541,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[8540, 8538])).
% 2.44/2.67 tff(8542,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8543,plain,
% 2.44/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8542, 8541])).
% 2.44/2.67 tff(8544,plain,
% 2.44/2.67 ($false),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8543, 171, 1188, 376, 2852, 357])).
% 2.44/2.67 tff(8545,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.67 tff(8546,plain,
% 2.44/2.67 (~b(s(s(s(z))), s(z))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8545, 8537, 357, 376])).
% 2.44/2.67 tff(8547,plain,
% 2.44/2.67 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[2842, 8536, 2839])).
% 2.44/2.67 tff(8548,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8549,plain,
% 2.44/2.67 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), 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(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8550,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.67 inference(monotonicity,[status(thm)],[8549])).
% 2.44/2.67 tff(8551,plain,
% 2.44/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.67 inference(transitivity,[status(thm)],[8550, 8548])).
% 2.44/2.67 tff(8552,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.67 inference(quant_inst,[status(thm)],[])).
% 2.44/2.67 tff(8553,plain,
% 2.44/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.67 inference(modus_ponens,[status(thm)],[8552, 8551])).
% 2.44/2.67 tff(8554,plain,
% 2.44/2.67 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[8553, 106, 260, 2604, 1357])).
% 2.44/2.67 tff(8555,plain,
% 2.44/2.67 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.67 inference(unit_resolution,[status(thm)],[4240, 25, 8554, 8230])).
% 2.44/2.67 tff(8556,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(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)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8557,plain,
% 2.44/2.67 (((~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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(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)))))))),
% 2.44/2.67 inference(rewrite,[status(thm)],[])).
% 2.44/2.67 tff(8558,plain,
% 2.44/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(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))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8557])).
% 2.44/2.68 tff(8559,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(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)))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8558, 8556])).
% 2.44/2.68 tff(8560,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8561,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8560, 8559])).
% 2.44/2.68 tff(8562,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8561, 171, 1976, 376, 8555, 8547])).
% 2.44/2.68 tff(8563,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(8564,plain,
% 2.44/2.68 (~b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8563, 2604, 260, 1357, 376, 2264, 502])).
% 2.44/2.68 tff(8565,plain,
% 2.44/2.68 (r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1996, 8564])).
% 2.44/2.68 tff(8566,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8567,plain,
% 2.44/2.68 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8568,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8567])).
% 2.44/2.68 tff(8569,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8568, 8566])).
% 2.44/2.68 tff(8570,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8571,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8570, 8569])).
% 2.44/2.68 tff(8572,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8571, 106, 1357, 502, 1998, 747])).
% 2.44/2.68 tff(8573,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(8574,plain,
% 2.44/2.68 (~r(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8573, 8565, 502, 1357])).
% 2.44/2.68 tff(8575,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1173, 8574, 8546])).
% 2.44/2.68 tff(8576,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), 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(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(8577,plain,
% 2.44/2.68 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8576, 1357, 502, 357, 376, 260])).
% 2.44/2.68 tff(8578,plain,
% 2.44/2.68 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2614, 8577])).
% 2.44/2.68 tff(8579,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8580,plain,
% 2.44/2.68 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8581,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8580])).
% 2.44/2.68 tff(8582,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8581, 8579])).
% 2.44/2.68 tff(8583,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8584,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8583, 8582])).
% 2.44/2.68 tff(8585,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8584, 171, 8578, 1275, 159, 1313])).
% 2.44/2.68 tff(8586,plain,
% 2.44/2.68 (r(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1173, 8585])).
% 2.44/2.68 tff(8587,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8588,plain,
% 2.44/2.68 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8589,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8588])).
% 2.44/2.68 tff(8590,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8589, 8587])).
% 2.44/2.68 tff(8591,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8592,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8591, 8590])).
% 2.44/2.68 tff(8593,plain,
% 2.44/2.68 (~b(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8592, 171, 8578, 1275, 159, 1313])).
% 2.44/2.68 tff(8594,plain,
% 2.44/2.68 (r(s(z), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1996, 8593])).
% 2.44/2.68 tff(8595,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8573, 8594, 8586, 502, 1357])).
% 2.44/2.68 tff(8596,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(8597,plain,
% 2.44/2.68 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8596, 502, 1275, 8195, 8525, 8527, 8513, 8523])).
% 2.44/2.68 tff(8598,plain,
% 2.44/2.68 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1368, 8597])).
% 2.44/2.68 tff(8599,plain,
% 2.44/2.68 (~b(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[6865, 171, 838, 1384, 1313])).
% 2.44/2.68 tff(8600,plain,
% 2.44/2.68 (r(s(s(s(z))), z)),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[953, 25, 194, 8599])).
% 2.44/2.68 tff(8601,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8602,plain,
% 2.44/2.68 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8603,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8602])).
% 2.44/2.68 tff(8604,plain,
% 2.44/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8603, 8601])).
% 2.44/2.68 tff(8605,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8606,plain,
% 2.44/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8605, 8604])).
% 2.44/2.68 tff(8607,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8606, 171, 838, 1275, 1384])).
% 2.44/2.68 tff(8608,plain,
% 2.44/2.68 (r(s(s(s(z))), s(z))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[1173, 8607])).
% 2.44/2.68 tff(8609,plain,
% 2.44/2.68 ($false),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[794, 106, 96, 95, 8608, 8600])).
% 2.44/2.68 tff(8610,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.68 tff(8611,plain,
% 2.44/2.68 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8610, 8598, 95, 96, 8525, 1275])).
% 2.44/2.68 tff(8612,plain,
% 2.44/2.68 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2614, 8611])).
% 2.44/2.68 tff(8613,plain,
% 2.44/2.68 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8535, 8612, 502, 8523])).
% 2.44/2.68 tff(8614,plain,
% 2.44/2.68 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[2842, 8613, 2264])).
% 2.44/2.68 tff(8615,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8616,plain,
% 2.44/2.68 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(rewrite,[status(thm)],[])).
% 2.44/2.68 tff(8617,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.44/2.68 inference(monotonicity,[status(thm)],[8616])).
% 2.44/2.68 tff(8618,plain,
% 2.44/2.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.44/2.68 inference(transitivity,[status(thm)],[8617, 8615])).
% 2.44/2.68 tff(8619,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.44/2.68 inference(quant_inst,[status(thm)],[])).
% 2.44/2.68 tff(8620,plain,
% 2.44/2.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.44/2.68 inference(modus_ponens,[status(thm)],[8619, 8618])).
% 2.44/2.68 tff(8621,plain,
% 2.44/2.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.68 inference(unit_resolution,[status(thm)],[8620, 106, 8523, 8612, 502])).
% 2.44/2.68 tff(8622,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6475, 8621])).
% 2.44/2.69 tff(8623,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8624,plain,
% 2.44/2.69 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8625,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8624])).
% 2.44/2.69 tff(8626,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[8625, 8623])).
% 2.44/2.69 tff(8627,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(8628,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[8627, 8626])).
% 2.44/2.69 tff(8629,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8628, 171, 83, 8598, 8622, 8614])).
% 2.44/2.69 tff(8630,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(8631,plain,
% 2.44/2.69 (~r(s(s(s(s(s(z))))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8630, 83, 95, 96, 1275])).
% 2.44/2.69 tff(8632,plain,
% 2.44/2.69 (b(s(s(s(s(s(z))))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[479, 8631])).
% 2.44/2.69 tff(8633,plain,
% 2.44/2.69 (~b(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8053, 8632, 1275, 83])).
% 2.44/2.69 tff(8634,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[321, 8633, 255])).
% 2.44/2.69 tff(8635,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6875, 8634, 95, 96])).
% 2.44/2.69 tff(8636,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), z)),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[274, 8635])).
% 2.44/2.69 tff(8637,plain,
% 2.44/2.69 (~b(s(z), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6394, 3686, 83, 4])).
% 2.44/2.69 tff(8638,plain,
% 2.44/2.69 (~r(s(z), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4309, 3686, 96, 83, 159, 263])).
% 2.44/2.69 tff(8639,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[454, 8638, 8637, 254])).
% 2.44/2.69 tff(8640,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(8641,plain,
% 2.44/2.69 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8640, 83, 96, 8195, 8634, 8632])).
% 2.44/2.69 tff(8642,plain,
% 2.44/2.69 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[3668, 8641])).
% 2.44/2.69 tff(8643,plain,
% 2.44/2.69 (~r(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8073, 8634, 95, 96])).
% 2.44/2.69 tff(8644,plain,
% 2.44/2.69 (b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[244, 8643])).
% 2.44/2.69 tff(8645,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8646,plain,
% 2.44/2.69 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8647,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8646])).
% 2.44/2.69 tff(8648,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[8647, 8645])).
% 2.44/2.69 tff(8649,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(8650,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[8649, 8648])).
% 2.44/2.69 tff(8651,plain,
% 2.44/2.69 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8650, 171, 8644, 1275, 8632])).
% 2.44/2.69 tff(8652,plain,
% 2.44/2.69 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[205, 8651])).
% 2.44/2.69 tff(8653,plain,
% 2.44/2.69 (~r(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8073, 263, 95, 96])).
% 2.44/2.69 tff(8654,plain,
% 2.44/2.69 (b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[244, 8653])).
% 2.44/2.69 tff(8655,plain,
% 2.44/2.69 (~r(z, s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6419, 554, 95, 501])).
% 2.44/2.69 tff(8656,plain,
% 2.44/2.69 (b(z, s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[124, 8655])).
% 2.44/2.69 tff(8657,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8149, 554, 501, 263])).
% 2.44/2.69 tff(8658,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[374, 8657, 355])).
% 2.44/2.69 tff(8659,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6307, 8658, 5188, 8656, 8654, 6877])).
% 2.44/2.69 tff(8660,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(8661,plain,
% 2.44/2.69 (~r(s(z), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8660, 8652, 8634, 96, 95])).
% 2.44/2.69 tff(8662,plain,
% 2.44/2.69 (b(s(z), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[550, 8661])).
% 2.44/2.69 tff(8663,plain,
% 2.44/2.69 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8081, 171, 8644, 1275, 8632])).
% 2.44/2.69 tff(8664,plain,
% 2.44/2.69 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[225, 8663])).
% 2.44/2.69 tff(8665,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8123, 106, 8642, 8664, 8652])).
% 2.44/2.69 tff(8666,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[374, 8665, 355])).
% 2.44/2.69 tff(8667,plain,
% 2.44/2.69 (~b(s(z), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6253, 8666, 8644, 8662])).
% 2.44/2.69 tff(8668,plain,
% 2.44/2.69 (r(s(z), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[454, 8667, 254])).
% 2.44/2.69 tff(8669,plain,
% 2.44/2.69 (~r(z, s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[6081, 8668, 95, 8642])).
% 2.44/2.69 tff(8670,plain,
% 2.44/2.69 (b(z, s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[293, 8669])).
% 2.44/2.69 tff(8671,plain,
% 2.44/2.69 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8131, 106, 8642, 8664, 8652])).
% 2.44/2.69 tff(8672,plain,
% 2.44/2.69 (b(s(s(z)), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[351, 8671])).
% 2.44/2.69 tff(8673,plain,
% 2.44/2.69 (~b(z, s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[5981, 8670, 8666, 8672])).
% 2.44/2.69 tff(8674,plain,
% 2.44/2.69 (r(z, s(s(z)))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[124, 8673])).
% 2.44/2.69 tff(8675,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8676,plain,
% 2.44/2.69 (((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8677,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8676])).
% 2.44/2.69 tff(8678,plain,
% 2.44/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[8677, 8675])).
% 2.44/2.69 tff(8679,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(8680,plain,
% 2.44/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[8679, 8678])).
% 2.44/2.69 tff(8681,plain,
% 2.44/2.69 (~r(z, s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8680, 106, 8674, 8664, 8652])).
% 2.44/2.69 tff(8682,plain,
% 2.44/2.69 (b(z, s(s(s(s(s(z))))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[498, 8681])).
% 2.44/2.69 tff(8683,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8684,plain,
% 2.44/2.69 (((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8685,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8684])).
% 2.44/2.69 tff(8686,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[8685, 8683])).
% 2.44/2.69 tff(8687,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), 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)))),
% 2.44/2.69 inference(quant_inst,[status(thm)],[])).
% 2.44/2.69 tff(8688,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.44/2.69 inference(modus_ponens,[status(thm)],[8687, 8686])).
% 2.44/2.69 tff(8689,plain,
% 2.44/2.69 ($false),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8688, 171, 83, 8195, 8682, 8670, 8636])).
% 2.44/2.69 tff(8690,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.69 tff(8691,plain,
% 2.44/2.69 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8690, 96, 95, 1275])).
% 2.44/2.69 tff(8692,plain,
% 2.44/2.69 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[427, 8691])).
% 2.44/2.69 tff(8693,plain,
% 2.44/2.69 (~r(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[4679, 502, 96, 95])).
% 2.44/2.69 tff(8694,plain,
% 2.44/2.69 (b(s(s(z)), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[244, 8693])).
% 2.44/2.69 tff(8695,plain,
% 2.44/2.69 (~r(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[8073, 2, 95, 96])).
% 2.44/2.69 tff(8696,plain,
% 2.44/2.69 (b(s(s(s(s(z)))), s(z))),
% 2.44/2.69 inference(unit_resolution,[status(thm)],[321, 8695, 255])).
% 2.44/2.69 tff(8697,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8698,plain,
% 2.44/2.69 (((~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), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(rewrite,[status(thm)],[])).
% 2.44/2.69 tff(8699,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.44/2.69 inference(monotonicity,[status(thm)],[8698])).
% 2.44/2.69 tff(8700,plain,
% 2.44/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.44/2.69 inference(transitivity,[status(thm)],[8699, 8697])).
% 2.44/2.69 tff(8701,plain,
% 2.44/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.44/2.70 inference(quant_inst,[status(thm)],[])).
% 2.44/2.70 tff(8702,plain,
% 2.44/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[8701, 8700])).
% 2.44/2.70 tff(8703,plain,
% 2.44/2.70 ($false),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[8702, 171, 3686, 1275, 4, 357])).
% 2.44/2.70 tff(8704,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.70 tff(8705,plain,
% 2.44/2.70 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[8704, 8696, 1275, 4])).
% 2.44/2.70 tff(8706,plain,
% 2.44/2.70 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[3668, 8705])).
% 2.44/2.70 tff(8707,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(8708,plain,
% 2.44/2.70 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.44/2.70 inference(rewrite,[status(thm)],[])).
% 2.44/2.70 tff(8709,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.44/2.70 inference(monotonicity,[status(thm)],[8708])).
% 2.44/2.70 tff(8710,plain,
% 2.44/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.44/2.70 inference(transitivity,[status(thm)],[8709, 8707])).
% 2.44/2.70 tff(8711,plain,
% 2.44/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.44/2.70 inference(quant_inst,[status(thm)],[])).
% 2.44/2.70 tff(8712,plain,
% 2.44/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.44/2.70 inference(modus_ponens,[status(thm)],[8711, 8710])).
% 2.44/2.70 tff(8713,plain,
% 2.44/2.70 ($false),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[8712, 106, 260, 5609, 1288, 2118])).
% 2.44/2.70 tff(8714,plain,((~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))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.44/2.70 tff(8715,plain,
% 2.44/2.70 (~r(s(s(s(s(z)))), z)),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[8714, 1288, 5609, 260])).
% 2.44/2.70 tff(8716,plain,
% 2.44/2.70 (b(s(s(s(s(z)))), z)),
% 2.44/2.70 inference(unit_resolution,[status(thm)],[274, 8715])).
% 2.54/2.70 tff(8717,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8718,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8719,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8718, 8717])).
% 2.54/2.70 tff(8720,plain,
% 2.54/2.70 (~r(z, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8719, 106, 260, 5609, 1288])).
% 2.54/2.70 tff(8721,plain,
% 2.54/2.70 (b(z, s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[293, 8720])).
% 2.54/2.70 tff(8722,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8723,plain,
% 2.54/2.70 (((~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)))), z)) | (~b(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)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8724,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(s(z))))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[8723])).
% 2.54/2.70 tff(8725,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(s(z)))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[8724, 8722])).
% 2.54/2.70 tff(8726,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8727,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z, s(s(s(s(z))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8726, 8725])).
% 2.54/2.70 tff(8728,plain,
% 2.54/2.70 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8727, 171, 1, 8721, 8716])).
% 2.54/2.70 tff(8729,plain,
% 2.54/2.70 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[351, 8728])).
% 2.54/2.70 tff(8730,plain,
% 2.54/2.70 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2535, 8721, 1, 8716])).
% 2.54/2.70 tff(8731,plain,
% 2.54/2.70 (r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[374, 8730, 355])).
% 2.54/2.70 tff(8732,plain,
% 2.54/2.70 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6526, 106, 5609, 8731, 8729])).
% 2.54/2.70 tff(8733,plain,
% 2.54/2.70 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[205, 8732])).
% 2.54/2.70 tff(8734,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8735,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8736,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8735, 8734])).
% 2.54/2.70 tff(8737,plain,
% 2.54/2.70 (~r(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8736, 106, 5609, 2604, 1288])).
% 2.54/2.70 tff(8738,plain,
% 2.54/2.70 (b(s(s(s(z))), z)),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[953, 25, 194, 8737])).
% 2.54/2.70 tff(8739,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8740,plain,
% 2.54/2.70 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), 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(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8741,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[8740])).
% 2.54/2.70 tff(8742,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[8741, 8739])).
% 2.54/2.70 tff(8743,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8744,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8743, 8742])).
% 2.54/2.70 tff(8745,plain,
% 2.54/2.70 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8744, 106, 260, 5609, 2604])).
% 2.54/2.70 tff(8746,plain,
% 2.54/2.70 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2842, 8745, 2264])).
% 2.54/2.70 tff(8747,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8748,plain,
% 2.54/2.70 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8749,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[8748])).
% 2.54/2.70 tff(8750,plain,
% 2.54/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.70 inference(transitivity,[status(thm)],[8749, 8747])).
% 2.54/2.70 tff(8751,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8752,plain,
% 2.54/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8751, 8750])).
% 2.54/2.70 tff(8753,plain,
% 2.54/2.70 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8752, 106, 260, 5609, 2604])).
% 2.54/2.70 tff(8754,plain,
% 2.54/2.70 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[6475, 8753])).
% 2.54/2.70 tff(8755,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8756,plain,
% 2.54/2.70 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(s(z)))), s(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)))),
% 2.54/2.70 inference(rewrite,[status(thm)],[])).
% 2.54/2.70 tff(8757,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 2.54/2.70 inference(monotonicity,[status(thm)],[8756])).
% 2.54/2.70 tff(8758,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(transitivity,[status(thm)],[8757, 8755])).
% 2.54/2.70 tff(8759,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 2.54/2.70 inference(quant_inst,[status(thm)],[])).
% 2.54/2.70 tff(8760,plain,
% 2.54/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 2.54/2.70 inference(modus_ponens,[status(thm)],[8759, 8758])).
% 2.54/2.70 tff(8761,plain,
% 2.54/2.70 ($false),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8760, 171, 8754, 8746, 8738, 8721])).
% 2.54/2.70 tff(8762,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.70 tff(8763,plain,
% 2.54/2.70 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[8762, 1288, 5609, 260])).
% 2.54/2.70 tff(8764,plain,
% 2.54/2.70 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.70 inference(unit_resolution,[status(thm)],[2614, 8763])).
% 2.54/2.70 tff(8765,plain,
% 2.54/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8766,plain,
% 2.54/2.71 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), 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(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8767,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8766])).
% 2.54/2.71 tff(8768,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8767, 8765])).
% 2.54/2.71 tff(8769,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8770,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8769, 8768])).
% 2.54/2.71 tff(8771,plain,
% 2.54/2.71 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8770, 171, 8764, 1275, 4, 8733])).
% 2.54/2.71 tff(8772,plain,
% 2.54/2.71 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[2642, 8771])).
% 2.54/2.71 tff(8773,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8774,plain,
% 2.54/2.71 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8775,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8774])).
% 2.54/2.71 tff(8776,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8775, 8773])).
% 2.54/2.71 tff(8777,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8778,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8777, 8776])).
% 2.54/2.71 tff(8779,plain,
% 2.54/2.71 (~b(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8778, 171, 8764, 1275, 4])).
% 2.54/2.71 tff(8780,plain,
% 2.54/2.71 (r(s(z), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1996, 8779])).
% 2.54/2.71 tff(8781,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8782,plain,
% 2.54/2.71 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8783,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8782])).
% 2.54/2.71 tff(8784,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8783, 8781])).
% 2.54/2.71 tff(8785,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8786,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8785, 8784])).
% 2.54/2.71 tff(8787,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8786, 106, 554, 2, 1199, 1998])).
% 2.54/2.71 tff(8788,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(8789,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8788, 8780, 8772, 554, 2])).
% 2.54/2.71 tff(8790,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(8791,plain,
% 2.54/2.71 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8790, 2, 554, 1275, 4, 8692, 8706, 5188])).
% 2.54/2.71 tff(8792,plain,
% 2.54/2.71 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[498, 8791])).
% 2.54/2.71 tff(8793,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8794,plain,
% 2.54/2.71 (((~b(s(z), s(s(s(s(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(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8795,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8794])).
% 2.54/2.71 tff(8796,plain,
% 2.54/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8795, 8793])).
% 2.54/2.71 tff(8797,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), 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)))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8798,plain,
% 2.54/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8797, 8796])).
% 2.54/2.71 tff(8799,plain,
% 2.54/2.71 ($false),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8798, 171, 1, 1275, 4, 160, 1313])).
% 2.54/2.71 tff(8800,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(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)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.71 tff(8801,plain,
% 2.54/2.71 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8800, 8792, 1275, 4, 5188])).
% 2.54/2.71 tff(8802,plain,
% 2.54/2.71 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[205, 8801])).
% 2.54/2.71 tff(8803,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8804,plain,
% 2.54/2.71 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8805,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8804])).
% 2.54/2.71 tff(8806,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8805, 8803])).
% 2.54/2.71 tff(8807,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8808,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8807, 8806])).
% 2.54/2.71 tff(8809,plain,
% 2.54/2.71 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8808, 106, 8706, 8692, 8802])).
% 2.54/2.71 tff(8810,plain,
% 2.54/2.71 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[351, 8809])).
% 2.54/2.71 tff(8811,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8812,plain,
% 2.54/2.71 (((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8813,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.54/2.71 inference(monotonicity,[status(thm)],[8812])).
% 2.54/2.71 tff(8814,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.54/2.71 inference(transitivity,[status(thm)],[8813, 8811])).
% 2.54/2.71 tff(8815,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.54/2.71 inference(quant_inst,[status(thm)],[])).
% 2.54/2.71 tff(8816,plain,
% 2.54/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.54/2.71 inference(modus_ponens,[status(thm)],[8815, 8814])).
% 2.54/2.71 tff(8817,plain,
% 2.54/2.71 (~r(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8816, 106, 554, 96, 2])).
% 2.54/2.71 tff(8818,plain,
% 2.54/2.71 (b(z, s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[124, 8817])).
% 2.54/2.71 tff(8819,plain,
% 2.54/2.71 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1163, 106, 8706, 8692, 8802])).
% 2.54/2.71 tff(8820,plain,
% 2.54/2.71 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[374, 8819, 355])).
% 2.54/2.71 tff(8821,plain,
% 2.54/2.71 (~b(z, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[5981, 8820, 8818, 8810])).
% 2.54/2.71 tff(8822,plain,
% 2.54/2.71 (r(z, s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[293, 8821])).
% 2.54/2.71 tff(8823,plain,
% 2.54/2.71 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[6081, 8822, 95, 8706])).
% 2.54/2.71 tff(8824,plain,
% 2.54/2.71 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[454, 8823, 254])).
% 2.54/2.71 tff(8825,plain,
% 2.54/2.71 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[8610, 838, 95, 96, 1313, 1275])).
% 2.54/2.71 tff(8826,plain,
% 2.54/2.71 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.71 inference(unit_resolution,[status(thm)],[1368, 8825])).
% 2.54/2.71 tff(8827,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8828,plain,
% 2.54/2.71 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.71 inference(rewrite,[status(thm)],[])).
% 2.54/2.71 tff(8829,plain,
% 2.54/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8828])).
% 2.54/2.72 tff(8830,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8829, 8827])).
% 2.54/2.72 tff(8831,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8832,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8831, 8830])).
% 2.54/2.72 tff(8833,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8832, 106, 260, 5609, 1357, 2828])).
% 2.54/2.72 tff(8834,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(8835,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8834, 8826, 8692, 260])).
% 2.54/2.72 tff(8836,plain,
% 2.54/2.72 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2842, 8835, 2264])).
% 2.54/2.72 tff(8837,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8545, 8836, 8696, 376])).
% 2.54/2.72 tff(8838,plain,
% 2.54/2.72 (r(s(s(s(z))), s(z))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1173, 8837])).
% 2.54/2.72 tff(8839,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8840,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8841,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8840, 8839])).
% 2.54/2.72 tff(8842,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8841, 106, 5609, 1357, 6477, 747])).
% 2.54/2.72 tff(8843,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(8844,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8843, 8838, 8692, 8826])).
% 2.54/2.72 tff(8845,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6475, 8844])).
% 2.54/2.72 tff(8846,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(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(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(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(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8847,plain,
% 2.54/2.72 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(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(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8848,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(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(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8847])).
% 2.54/2.72 tff(8849,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(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(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8848, 8846])).
% 2.54/2.72 tff(8850,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8851,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8850, 8849])).
% 2.54/2.72 tff(8852,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8851, 171, 1976, 838, 376, 6462, 2852])).
% 2.54/2.72 tff(8853,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(8854,plain,
% 2.54/2.72 (~b(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8853, 8845, 376, 838, 8836])).
% 2.54/2.72 tff(8855,plain,
% 2.54/2.72 (r(s(z), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[1996, 8854])).
% 2.54/2.72 tff(8856,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8788, 8855, 554, 2])).
% 2.54/2.72 tff(8857,plain,
% 2.54/2.72 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2642, 8856])).
% 2.54/2.72 tff(8858,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8859,plain,
% 2.54/2.72 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8860,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8859])).
% 2.54/2.72 tff(8861,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8860, 8858])).
% 2.54/2.72 tff(8862,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(s(z)))), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8863,plain,
% 2.54/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8862, 8861])).
% 2.54/2.72 tff(8864,plain,
% 2.54/2.72 ($false),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8863, 171, 5188, 8857, 838, 8845, 356, 1313])).
% 2.54/2.72 tff(8865,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.72 tff(8866,plain,
% 2.54/2.72 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8865, 8820, 8792, 554, 2, 8824, 8706, 95, 96, 1275])).
% 2.54/2.72 tff(8867,plain,
% 2.54/2.72 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2614, 8866])).
% 2.54/2.72 tff(8868,plain,
% 2.54/2.72 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8752, 106, 8706, 8692, 8867])).
% 2.54/2.72 tff(8869,plain,
% 2.54/2.72 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[6475, 8868])).
% 2.54/2.72 tff(8870,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8871,plain,
% 2.54/2.72 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(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(z)))))) <=> ((~r(s(s(z)), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8872,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), 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(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8871])).
% 2.54/2.72 tff(8873,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8872, 8870])).
% 2.54/2.72 tff(8874,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8875,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8874, 8873])).
% 2.54/2.72 tff(8876,plain,
% 2.54/2.72 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8875, 106, 8692, 8867, 8802])).
% 2.54/2.72 tff(8877,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8878,plain,
% 2.54/2.72 (((~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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8879,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8878])).
% 2.54/2.72 tff(8880,plain,
% 2.54/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8879, 8877])).
% 2.54/2.72 tff(8881,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.72 inference(quant_inst,[status(thm)],[])).
% 2.54/2.72 tff(8882,plain,
% 2.54/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(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(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.54/2.72 inference(modus_ponens,[status(thm)],[8881, 8880])).
% 2.54/2.72 tff(8883,plain,
% 2.54/2.72 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8882, 106, 8692, 8867, 8802])).
% 2.54/2.72 tff(8884,plain,
% 2.54/2.72 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[2642, 8883])).
% 2.54/2.72 tff(8885,plain,
% 2.54/2.72 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[979, 25, 2569])).
% 2.54/2.72 tff(8886,plain,
% 2.54/2.72 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.72 inference(unit_resolution,[status(thm)],[8885, 900])).
% 2.54/2.72 tff(8887,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8888,plain,
% 2.54/2.72 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(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(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.72 inference(rewrite,[status(thm)],[])).
% 2.54/2.72 tff(8889,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.54/2.72 inference(monotonicity,[status(thm)],[8888])).
% 2.54/2.72 tff(8890,plain,
% 2.54/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.54/2.72 inference(transitivity,[status(thm)],[8889, 8887])).
% 2.54/2.73 tff(8891,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(8892,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[8891, 8890])).
% 2.54/2.73 tff(8893,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8892, 171, 2705, 6462, 356, 8886])).
% 2.54/2.73 tff(8894,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | r(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8895,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8894, 8884, 8876, 8820, 8869])).
% 2.54/2.73 tff(8896,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8897,plain,
% 2.54/2.73 (~r(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8896, 4, 95, 96, 1275, 554])).
% 2.54/2.73 tff(8898,plain,
% 2.54/2.73 (b(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[244, 8897])).
% 2.54/2.73 tff(8899,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8650, 171, 8898, 1275, 4])).
% 2.54/2.73 tff(8900,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[205, 8899])).
% 2.54/2.73 tff(8901,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8660, 8900, 554, 96, 95])).
% 2.54/2.73 tff(8902,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[321, 8901, 255])).
% 2.54/2.73 tff(8903,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8704, 8902, 1275, 4])).
% 2.54/2.73 tff(8904,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3668, 8903])).
% 2.54/2.73 tff(8905,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[587, 8904, 8898, 8900, 554, 8902])).
% 2.54/2.73 tff(8906,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[374, 8905, 355])).
% 2.54/2.73 tff(8907,plain,
% 2.54/2.73 (~r(z, s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6419, 8900, 95, 554])).
% 2.54/2.73 tff(8908,plain,
% 2.54/2.73 (b(z, s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[124, 8907])).
% 2.54/2.73 tff(8909,plain,
% 2.54/2.73 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[445, 8902, 4, 8898])).
% 2.54/2.73 tff(8910,plain,
% 2.54/2.73 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[454, 8909, 254])).
% 2.54/2.73 tff(8911,plain,
% 2.54/2.73 (~r(z, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6081, 8910, 95, 8904])).
% 2.54/2.73 tff(8912,plain,
% 2.54/2.73 (b(z, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[293, 8911])).
% 2.54/2.73 tff(8913,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[5981, 8912, 8908, 8906])).
% 2.54/2.73 tff(8914,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[351, 8913])).
% 2.54/2.73 tff(8915,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8808, 106, 8904, 8692, 8900, 8914])).
% 2.54/2.73 tff(8916,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8917,plain,
% 2.54/2.73 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8916, 554, 95, 1275, 96])).
% 2.54/2.73 tff(8918,plain,
% 2.54/2.73 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[479, 8917])).
% 2.54/2.73 tff(8919,plain,
% 2.54/2.73 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[562, 106, 554, 96, 8918])).
% 2.54/2.73 tff(8920,plain,
% 2.54/2.73 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[498, 8919])).
% 2.54/2.73 tff(8921,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8043, 8918, 95, 96])).
% 2.54/2.73 tff(8922,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[145, 8921])).
% 2.54/2.73 tff(8923,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7054, 8918, 8692, 554])).
% 2.54/2.73 tff(8924,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[321, 8923, 255])).
% 2.54/2.73 tff(8925,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8926,plain,
% 2.54/2.73 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8927,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[8926])).
% 2.54/2.73 tff(8928,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.73 inference(transitivity,[status(thm)],[8927, 8925])).
% 2.54/2.73 tff(8929,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(8930,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[8929, 8928])).
% 2.54/2.73 tff(8931,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8930, 171, 3686, 1275, 159, 357, 1313])).
% 2.54/2.73 tff(8932,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8933,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8932, 8920, 1275, 8922, 8924])).
% 2.54/2.73 tff(8934,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3668, 8933])).
% 2.54/2.73 tff(8935,plain,
% 2.54/2.73 (~r(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[4679, 8918, 96, 95])).
% 2.54/2.73 tff(8936,plain,
% 2.54/2.73 (b(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[244, 8935])).
% 2.54/2.73 tff(8937,plain,
% 2.54/2.73 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7068, 8934, 8692, 8918])).
% 2.54/2.73 tff(8938,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[454, 8937, 254])).
% 2.54/2.73 tff(8939,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[566, 8938, 8936, 8924])).
% 2.54/2.73 tff(8940,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[374, 8939, 355])).
% 2.54/2.73 tff(8941,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[587, 8940, 8936, 8934, 554, 8924])).
% 2.54/2.73 tff(8942,plain,
% 2.54/2.73 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[205, 8941])).
% 2.54/2.73 tff(8943,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6917, 171, 5188, 8942, 8922, 8920])).
% 2.54/2.73 tff(8944,plain,((~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8945,plain,
% 2.54/2.73 (~r(s(z), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8944, 96, 1275, 95])).
% 2.54/2.73 tff(8946,plain,
% 2.54/2.73 (b(s(z), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[550, 8945])).
% 2.54/2.73 tff(8947,plain,
% 2.54/2.73 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3978, 8525, 95, 96, 502])).
% 2.54/2.73 tff(8948,plain,
% 2.54/2.73 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[321, 8947, 255])).
% 2.54/2.73 tff(8949,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6512, 8948, 8946, 8694])).
% 2.54/2.73 tff(8950,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[351, 8949])).
% 2.54/2.73 tff(8951,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8043, 502, 95, 96])).
% 2.54/2.73 tff(8952,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), z)),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[145, 8951])).
% 2.54/2.73 tff(8953,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8932, 8948, 1275, 8952, 8525])).
% 2.54/2.73 tff(8954,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3668, 8953])).
% 2.54/2.73 tff(8955,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[510, 8950, 502, 8954])).
% 2.54/2.73 tff(8956,plain,
% 2.54/2.73 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[205, 8955])).
% 2.54/2.73 tff(8957,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[365, 8948, 8946, 8694])).
% 2.54/2.73 tff(8958,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[374, 8957, 355])).
% 2.54/2.73 tff(8959,plain,
% 2.54/2.73 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[6821, 8958, 8692, 502])).
% 2.54/2.73 tff(8960,plain,
% 2.54/2.73 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[454, 8959, 254])).
% 2.54/2.73 tff(8961,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8596, 8960, 1275, 502, 8952, 8948, 8525, 8954])).
% 2.54/2.73 tff(8962,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[1368, 8961])).
% 2.54/2.73 tff(8963,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8964,plain,
% 2.54/2.73 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), 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(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8965,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[8964])).
% 2.54/2.73 tff(8966,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[8965, 8963])).
% 2.54/2.73 tff(8967,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(8968,plain,
% 2.54/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[8967, 8966])).
% 2.54/2.73 tff(8969,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8968, 171, 323, 1275, 1384, 160, 207])).
% 2.54/2.73 tff(8970,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), 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(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8971,plain,
% 2.54/2.73 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8970, 8962, 1275, 8946, 8956])).
% 2.54/2.73 tff(8972,plain,
% 2.54/2.73 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[225, 8971])).
% 2.54/2.73 tff(8973,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8974,plain,
% 2.54/2.73 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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(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(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8975,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[8974])).
% 2.54/2.73 tff(8976,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[8975, 8973])).
% 2.54/2.73 tff(8977,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(8978,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[8977, 8976])).
% 2.54/2.73 tff(8979,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8978, 106, 8954, 8692, 8972, 8950])).
% 2.54/2.73 tff(8980,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(8981,plain,
% 2.54/2.73 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8980, 96, 95, 1275])).
% 2.54/2.73 tff(8982,plain,
% 2.54/2.73 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[479, 8981])).
% 2.54/2.73 tff(8983,plain,
% 2.54/2.73 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8704, 3686, 1275, 8982])).
% 2.54/2.73 tff(8984,plain,
% 2.54/2.73 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[321, 8983, 255])).
% 2.54/2.73 tff(8985,plain,
% 2.54/2.73 (~r(z, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[281, 106, 96, 95, 8984])).
% 2.54/2.73 tff(8986,plain,
% 2.54/2.73 (b(z, s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[293, 8985])).
% 2.54/2.73 tff(8987,plain,
% 2.54/2.73 (~r(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[8073, 8984, 95, 96])).
% 2.54/2.73 tff(8988,plain,
% 2.54/2.73 (b(s(s(z)), s(z))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[244, 8987])).
% 2.54/2.73 tff(8989,plain,
% 2.54/2.73 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[3673, 8988, 8946, 8982])).
% 2.54/2.73 tff(8990,plain,
% 2.54/2.73 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[205, 8989])).
% 2.54/2.73 tff(8991,plain,
% 2.54/2.73 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7170, 8990, 8692, 8984])).
% 2.54/2.73 tff(8992,plain,
% 2.54/2.73 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[351, 8991])).
% 2.54/2.73 tff(8993,plain,
% 2.54/2.73 (~b(z, s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[7159, 171, 8988, 3686, 8982, 8986, 8992])).
% 2.54/2.73 tff(8994,plain,
% 2.54/2.73 (r(z, s(s(z)))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[124, 8993])).
% 2.54/2.73 tff(8995,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8996,plain,
% 2.54/2.73 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(8997,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.54/2.73 inference(monotonicity,[status(thm)],[8996])).
% 2.54/2.73 tff(8998,plain,
% 2.54/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.54/2.73 inference(transitivity,[status(thm)],[8997, 8995])).
% 2.54/2.73 tff(8999,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 2.54/2.73 inference(quant_inst,[status(thm)],[])).
% 2.54/2.73 tff(9000,plain,
% 2.54/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.54/2.73 inference(modus_ponens,[status(thm)],[8999, 8998])).
% 2.54/2.73 tff(9001,plain,
% 2.54/2.73 ($false),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9000, 106, 600, 5609, 1288, 501])).
% 2.54/2.73 tff(9002,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.73 tff(9003,plain,
% 2.54/2.73 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[9002, 8994, 8692, 8990])).
% 2.54/2.73 tff(9004,plain,
% 2.54/2.73 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.73 inference(unit_resolution,[status(thm)],[498, 9003])).
% 2.54/2.73 tff(9005,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(9006,plain,
% 2.54/2.73 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.73 inference(rewrite,[status(thm)],[])).
% 2.54/2.73 tff(9007,plain,
% 2.54/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[9006])).
% 2.54/2.74 tff(9008,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[9007, 9005])).
% 2.54/2.74 tff(9009,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(9010,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[9009, 9008])).
% 2.54/2.74 tff(9011,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9010, 171, 3686, 1275, 8982, 9004, 8986])).
% 2.54/2.74 tff(9012,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9013,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9012, 96, 1275, 95])).
% 2.54/2.74 tff(9014,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3668, 9013])).
% 2.54/2.74 tff(9015,plain,
% 2.54/2.74 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8808, 106, 9014, 8692, 501])).
% 2.54/2.74 tff(9016,plain,
% 2.54/2.74 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[351, 9015])).
% 2.54/2.74 tff(9017,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1163, 106, 9014, 8692, 501])).
% 2.54/2.74 tff(9018,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[374, 9017, 355])).
% 2.54/2.74 tff(9019,plain,
% 2.54/2.74 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6253, 9018, 8946, 259])).
% 2.54/2.74 tff(9020,plain,
% 2.54/2.74 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[454, 9019, 254])).
% 2.54/2.74 tff(9021,plain,
% 2.54/2.74 (~r(z, s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6081, 9020, 95, 9014])).
% 2.54/2.74 tff(9022,plain,
% 2.54/2.74 (b(z, s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[293, 9021])).
% 2.54/2.74 tff(9023,plain,
% 2.54/2.74 (~b(z, s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5981, 9022, 9016, 9018])).
% 2.54/2.74 tff(9024,plain,
% 2.54/2.74 (r(z, s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[124, 9023])).
% 2.54/2.74 tff(9025,plain,
% 2.54/2.74 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9002, 9024, 8692, 501])).
% 2.54/2.74 tff(9026,plain,
% 2.54/2.74 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[498, 9025])).
% 2.54/2.74 tff(9027,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9028,plain,
% 2.54/2.74 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9029,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[9028])).
% 2.54/2.74 tff(9030,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[9029, 9027])).
% 2.54/2.74 tff(9031,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(9032,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[9031, 9030])).
% 2.54/2.74 tff(9033,plain,
% 2.54/2.74 (~b(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9032, 171, 838, 1275, 8982, 1313])).
% 2.54/2.74 tff(9034,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8834, 8826, 8692, 9014])).
% 2.54/2.74 tff(9035,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2842, 9034, 2264])).
% 2.54/2.74 tff(9036,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9037,plain,
% 2.54/2.74 (((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9038,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[9037])).
% 2.54/2.74 tff(9039,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[9038, 9036])).
% 2.54/2.74 tff(9040,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(9041,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[9040, 9039])).
% 2.54/2.74 tff(9042,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9041, 171, 8946, 838, 1275, 8982])).
% 2.54/2.74 tff(9043,plain,
% 2.54/2.74 (r(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1173, 9042])).
% 2.54/2.74 tff(9044,plain,
% 2.54/2.74 (~b(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8760, 171, 6462, 2852, 2527])).
% 2.54/2.74 tff(9045,plain,
% 2.54/2.74 (r(s(s(s(z))), z)),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[953, 25, 194, 9044])).
% 2.54/2.74 tff(9046,assumption,(z = s(s(s(z)))), introduced(assumption)).
% 2.54/2.74 tff(9047,plain,
% 2.54/2.74 (s(s(s(z))) = z),
% 2.54/2.74 inference(symmetry,[status(thm)],[9046])).
% 2.54/2.74 tff(9048,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[194, 9047])).
% 2.54/2.74 tff(9049,plain,(~(z = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9050,assumption,(~b(z, s(s(s(z))))), introduced(assumption)).
% 2.54/2.74 tff(9051,plain,
% 2.54/2.74 (r(z, s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8373, 25, 9050, 9049])).
% 2.54/2.74 tff(9052,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9053,plain,
% 2.54/2.74 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9054,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[9053])).
% 2.54/2.74 tff(9055,plain,
% 2.54/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.54/2.74 inference(transitivity,[status(thm)],[9054, 9052])).
% 2.54/2.74 tff(9056,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(9057,plain,
% 2.54/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[9056, 9055])).
% 2.54/2.74 tff(9058,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9057, 106, 95, 747, 9051, 9045])).
% 2.54/2.74 tff(9059,plain,(b(z, s(s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9060,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9059, 9043, 95, 2527, 9035, 9033])).
% 2.54/2.74 tff(9061,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8843, 9043, 8692, 8826])).
% 2.54/2.74 tff(9062,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6475, 9061, 9060])).
% 2.54/2.74 tff(9063,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9064,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9063, 9022, 95, 1275, 9026, 96])).
% 2.54/2.74 tff(9065,plain,
% 2.54/2.74 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2614, 9064])).
% 2.54/2.74 tff(9066,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8752, 106, 9014, 8692, 9065])).
% 2.54/2.74 tff(9067,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6475, 9066])).
% 2.54/2.74 tff(9068,plain,
% 2.54/2.74 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8875, 106, 8692, 9065, 501])).
% 2.54/2.74 tff(9069,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8882, 106, 8692, 9065, 501])).
% 2.54/2.74 tff(9070,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2642, 9069])).
% 2.54/2.74 tff(9071,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8894, 9070, 9068, 9018, 9067])).
% 2.54/2.74 tff(9072,plain,((~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9073,plain,
% 2.54/2.74 (~b(s(s(z)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9072, 501, 95, 1275, 96])).
% 2.54/2.74 tff(9074,plain,
% 2.54/2.74 (r(s(s(z)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[244, 9073])).
% 2.54/2.74 tff(9075,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8073, 9074, 95, 96])).
% 2.54/2.74 tff(9076,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[321, 9075, 255])).
% 2.54/2.74 tff(9077,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9078,plain,
% 2.54/2.74 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), 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(z))))),
% 2.54/2.74 inference(rewrite,[status(thm)],[])).
% 2.54/2.74 tff(9079,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.54/2.74 inference(monotonicity,[status(thm)],[9078])).
% 2.54/2.74 tff(9080,plain,
% 2.54/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(transitivity,[status(thm)],[9079, 9077])).
% 2.54/2.74 tff(9081,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.54/2.74 inference(quant_inst,[status(thm)],[])).
% 2.54/2.74 tff(9082,plain,
% 2.54/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.54/2.74 inference(modus_ponens,[status(thm)],[9081, 9080])).
% 2.54/2.74 tff(9083,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9082, 171, 8946, 9076, 9018, 9016])).
% 2.54/2.74 tff(9084,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9085,plain,
% 2.54/2.74 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9084, 96, 95, 1275])).
% 2.54/2.74 tff(9086,plain,
% 2.54/2.74 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[205, 9085])).
% 2.54/2.74 tff(9087,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1281, 171, 8946, 1275, 8982, 9086])).
% 2.54/2.74 tff(9088,plain,((~r(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9089,plain,
% 2.54/2.74 (~r(z, s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9088, 8041, 31])).
% 2.54/2.74 tff(9090,plain,
% 2.54/2.74 (b(z, s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[93, 9089])).
% 2.54/2.74 tff(9091,plain,
% 2.54/2.74 (~b(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8521, 3686, 1275, 83])).
% 2.54/2.74 tff(9092,plain,
% 2.54/2.74 (r(s(z), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[454, 9091, 254])).
% 2.54/2.74 tff(9093,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8249, 9092, 502, 3686])).
% 2.54/2.74 tff(9094,plain,
% 2.54/2.74 (b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1173, 9093])).
% 2.54/2.74 tff(9095,plain,
% 2.54/2.74 (~r(z, s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9088, 1275, 95])).
% 2.54/2.74 tff(9096,plain,
% 2.54/2.74 (b(z, s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[93, 9095])).
% 2.54/2.74 tff(9097,plain,
% 2.54/2.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8305, 1998, 83, 502, 9092, 8480])).
% 2.54/2.74 tff(9098,plain,
% 2.54/2.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1368, 9097])).
% 2.54/2.74 tff(9099,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8179, 9092, 83, 3686, 8480, 1275])).
% 2.54/2.74 tff(9100,plain,
% 2.54/2.74 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2614, 9099])).
% 2.54/2.74 tff(9101,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6485, 1998, 9100, 8480])).
% 2.54/2.74 tff(9102,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6475, 9101])).
% 2.54/2.74 tff(9103,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8315, 9102, 9098, 1275, 83, 9094, 3686])).
% 2.54/2.74 tff(9104,plain,((~r(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9105,plain,
% 2.54/2.74 (~r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9104, 3686, 83, 1275, 502])).
% 2.54/2.74 tff(9106,plain,
% 2.54/2.74 (b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1996, 9105])).
% 2.54/2.74 tff(9107,plain,
% 2.54/2.74 (~b(s(s(z)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8284, 9106, 9096, 9094])).
% 2.54/2.74 tff(9108,plain,
% 2.54/2.74 (r(s(s(z)), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[244, 9107])).
% 2.54/2.74 tff(9109,plain,
% 2.54/2.74 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8468, 9108, 502, 9092])).
% 2.54/2.74 tff(9110,plain,
% 2.54/2.74 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[225, 9109])).
% 2.54/2.74 tff(9111,plain,
% 2.54/2.74 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8483, 9110, 1275, 83, 9092, 3686, 9108])).
% 2.54/2.74 tff(9112,plain,
% 2.54/2.74 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[205, 9111])).
% 2.54/2.74 tff(9113,plain,
% 2.54/2.74 ($false),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5833, 106, 9108, 95, 502, 9112])).
% 2.54/2.74 tff(9114,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.74 tff(9115,plain,
% 2.54/2.74 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[9114, 502, 95, 1275, 83])).
% 2.54/2.74 tff(9116,plain,
% 2.54/2.74 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[3668, 9115])).
% 2.54/2.74 tff(9117,plain,
% 2.54/2.74 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[5552, 9116, 502, 95])).
% 2.54/2.74 tff(9118,plain,
% 2.54/2.74 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[321, 9117, 255])).
% 2.54/2.74 tff(9119,plain,
% 2.54/2.74 (~r(z, s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[6081, 3, 95, 9116])).
% 2.54/2.74 tff(9120,plain,
% 2.54/2.74 (b(z, s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[293, 9119])).
% 2.54/2.74 tff(9121,plain,
% 2.54/2.74 (~b(s(z), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[7254, 9120, 9096, 259, 9118])).
% 2.54/2.74 tff(9122,plain,
% 2.54/2.74 (r(s(z), s(s(z)))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[550, 9121])).
% 2.54/2.74 tff(9123,plain,
% 2.54/2.74 (~r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2836, 2828, 260, 3])).
% 2.54/2.74 tff(9124,plain,
% 2.54/2.74 (b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1996, 9123])).
% 2.54/2.74 tff(9125,plain,
% 2.54/2.74 (~b(s(s(s(z))), s(z))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8284, 9124, 3281, 259])).
% 2.54/2.74 tff(9126,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8535, 2828, 502, 260])).
% 2.54/2.74 tff(9127,plain,
% 2.54/2.74 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2614, 9126])).
% 2.54/2.74 tff(9128,plain,
% 2.54/2.74 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8213, 747, 502, 3])).
% 2.54/2.74 tff(9129,plain,
% 2.54/2.74 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1368, 9128])).
% 2.54/2.74 tff(9130,plain,
% 2.54/2.74 (~b(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[8446, 9129, 1275, 838])).
% 2.54/2.74 tff(9131,plain,
% 2.54/2.74 (r(s(z), s(s(s(z))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[1996, 9130])).
% 2.54/2.74 tff(9132,plain,
% 2.54/2.74 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.74 inference(unit_resolution,[status(thm)],[2836, 9131, 260, 3])).
% 2.54/2.75 tff(9133,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2842, 9132, 2264])).
% 2.54/2.75 tff(9134,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9135,plain,
% 2.54/2.75 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9136,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9135])).
% 2.54/2.75 tff(9137,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[9136, 9134])).
% 2.54/2.75 tff(9138,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(9139,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[9138, 9137])).
% 2.54/2.75 tff(9140,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9139, 106, 1998, 3, 6477, 747])).
% 2.54/2.75 tff(9141,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9142,plain,
% 2.54/2.75 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9141, 9131, 3, 747])).
% 2.54/2.75 tff(9143,plain,
% 2.54/2.75 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6475, 9142])).
% 2.54/2.75 tff(9144,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9145,plain,
% 2.54/2.75 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9146,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9145])).
% 2.54/2.75 tff(9147,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[9146, 9144])).
% 2.54/2.75 tff(9148,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(9149,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[9148, 9147])).
% 2.54/2.75 tff(9150,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9149, 171, 83, 838, 9129, 9143, 9133])).
% 2.54/2.75 tff(9151,plain,((~r(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9152,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(z))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9151, 9127, 83, 3, 260, 1275, 502])).
% 2.54/2.75 tff(9153,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[1173, 9152, 9125])).
% 2.54/2.75 tff(9154,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9155,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9154, 3, 83, 9116, 1275, 502, 9096, 259])).
% 2.54/2.75 tff(9156,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2842, 9155, 2264])).
% 2.54/2.75 tff(9157,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9158,plain,
% 2.54/2.75 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9159,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9158])).
% 2.54/2.75 tff(9160,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[9159, 9157])).
% 2.54/2.75 tff(9161,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(9162,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[9161, 9160])).
% 2.54/2.75 tff(9163,plain,
% 2.54/2.75 (~b(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9162, 171, 9096, 259, 83, 1275, 2527])).
% 2.54/2.75 tff(9164,plain,
% 2.54/2.75 (r(s(s(z)), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[157, 9163])).
% 2.54/2.75 tff(9165,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8416, 106, 554, 637, 95, 1975])).
% 2.54/2.75 tff(9166,plain,((~r(z, s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9167,plain,
% 2.54/2.75 (~r(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9166, 9164, 554, 95])).
% 2.54/2.75 tff(9168,plain,
% 2.54/2.75 (b(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8373, 25, 9167, 9049])).
% 2.54/2.75 tff(9169,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9170,plain,
% 2.54/2.75 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9171,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9170])).
% 2.54/2.75 tff(9172,plain,
% 2.54/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[9171, 9169])).
% 2.54/2.75 tff(9173,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(9174,plain,
% 2.54/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[9173, 9172])).
% 2.54/2.75 tff(9175,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9174, 171, 6462, 2852, 2527, 9168])).
% 2.54/2.75 tff(9176,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9177,plain,
% 2.54/2.75 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9176, 9156, 9120, 9122, 95, 259, 83, 1275])).
% 2.54/2.75 tff(9178,plain,
% 2.54/2.75 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[6475, 9177])).
% 2.54/2.75 tff(9179,plain,
% 2.54/2.75 (~b(s(s(s(s(s(z))))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8511, 3, 1275, 83, 502])).
% 2.54/2.75 tff(9180,plain,
% 2.54/2.75 (r(s(s(s(s(s(z))))), z)),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[145, 9179])).
% 2.54/2.75 tff(9181,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9182,plain,
% 2.54/2.75 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9183,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z)))))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9182])).
% 2.54/2.75 tff(9184,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.54/2.75 inference(transitivity,[status(thm)],[9183, 9181])).
% 2.54/2.75 tff(9185,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.75 inference(quant_inst,[status(thm)],[])).
% 2.54/2.75 tff(9186,plain,
% 2.54/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(z)))))),
% 2.54/2.75 inference(modus_ponens,[status(thm)],[9185, 9184])).
% 2.54/2.75 tff(9187,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9186, 106, 95, 502, 127, 1975])).
% 2.54/2.75 tff(9188,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9189,plain,
% 2.54/2.75 (~r(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9188, 9180, 502, 95])).
% 2.54/2.75 tff(9190,assumption,(~r(z, s(s(s(z))))), introduced(assumption)).
% 2.54/2.75 tff(9191,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8373, 25, 9190, 9050, 9049])).
% 2.54/2.75 tff(9192,plain,(b(z, s(s(s(z)))) | r(z, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9193,plain,
% 2.54/2.75 (b(z, s(s(s(z))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9192, 9189])).
% 2.54/2.75 tff(9194,plain,
% 2.54/2.75 ($false),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[8620, 106, 260, 2604, 502, 6477])).
% 2.54/2.75 tff(9195,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.75 tff(9196,plain,
% 2.54/2.75 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[9195, 9178, 502, 9116])).
% 2.54/2.75 tff(9197,plain,
% 2.54/2.75 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.75 inference(unit_resolution,[status(thm)],[2614, 9196])).
% 2.54/2.75 tff(9198,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9199,plain,
% 2.54/2.75 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.75 inference(rewrite,[status(thm)],[])).
% 2.54/2.75 tff(9200,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.75 inference(monotonicity,[status(thm)],[9199])).
% 2.54/2.75 tff(9201,plain,
% 2.54/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9200, 9198])).
% 2.54/2.76 tff(9202,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9203,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9202, 9201])).
% 2.54/2.76 tff(9204,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9203, 106, 95, 600, 502, 127])).
% 2.54/2.76 tff(9205,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(9206,plain,
% 2.54/2.76 (~r(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9205, 9180, 502, 95])).
% 2.54/2.76 tff(9207,plain,
% 2.54/2.76 (b(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[124, 9206])).
% 2.54/2.76 tff(9208,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9209,plain,
% 2.54/2.76 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), 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(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9210,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[9209])).
% 2.54/2.76 tff(9211,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9210, 9208])).
% 2.54/2.76 tff(9212,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9213,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9212, 9211])).
% 2.54/2.76 tff(9214,plain,
% 2.54/2.76 ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9213, 171, 259, 9207, 9197, 1275])).
% 2.54/2.76 tff(9215,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9214, 9193])).
% 2.54/2.76 tff(9216,plain,
% 2.54/2.76 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2642, 9215])).
% 2.54/2.76 tff(9217,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9218,plain,
% 2.54/2.76 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9219,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[9218])).
% 2.54/2.76 tff(9220,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9219, 9217])).
% 2.54/2.76 tff(9221,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9222,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9221, 9220])).
% 2.54/2.76 tff(9223,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9222, 106, 95, 502, 127, 1288])).
% 2.54/2.76 tff(9224,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(9225,plain,
% 2.54/2.76 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9224, 9180, 502, 95])).
% 2.54/2.76 tff(9226,plain,
% 2.54/2.76 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[498, 9225])).
% 2.54/2.76 tff(9227,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9228,plain,
% 2.54/2.76 (((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9229,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[9228])).
% 2.54/2.76 tff(9230,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9229, 9227])).
% 2.54/2.76 tff(9231,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9232,plain,
% 2.54/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9231, 9230])).
% 2.54/2.76 tff(9233,plain,
% 2.54/2.76 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9232, 171, 83, 9197, 9226, 9193])).
% 2.54/2.76 tff(9234,plain,
% 2.54/2.76 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[1368, 9233])).
% 2.54/2.76 tff(9235,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9236,plain,
% 2.54/2.76 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9237,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[9236])).
% 2.54/2.76 tff(9238,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9237, 9235])).
% 2.54/2.76 tff(9239,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9240,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9239, 9238])).
% 2.54/2.76 tff(9241,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9240, 106, 9116, 9234, 9216, 9178])).
% 2.54/2.76 tff(9242,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(9243,plain,
% 2.54/2.76 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9242, 259, 83, 1275, 502, 95])).
% 2.54/2.76 tff(9244,plain,
% 2.54/2.76 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[454, 9243, 254])).
% 2.54/2.76 tff(9245,plain,
% 2.54/2.76 (~b(s(s(z)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7100, 9244, 9096, 9118, 259])).
% 2.54/2.76 tff(9246,plain,
% 2.54/2.76 (r(s(s(z)), z)),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[157, 9245])).
% 2.54/2.76 tff(9247,plain,
% 2.54/2.76 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[566, 9244, 9118, 259])).
% 2.54/2.76 tff(9248,plain,
% 2.54/2.76 (r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[374, 9247, 355])).
% 2.54/2.76 tff(9249,plain,
% 2.54/2.76 (~r(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[5575, 5567, 95, 637])).
% 2.54/2.76 tff(9250,plain,
% 2.54/2.76 (b(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[550, 9249])).
% 2.54/2.76 tff(9251,plain,
% 2.54/2.76 (~r(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[6247, 5567, 569, 637])).
% 2.54/2.76 tff(9252,plain,
% 2.54/2.76 (b(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[124, 9251])).
% 2.54/2.76 tff(9253,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7045, 9252, 9250, 3281, 259])).
% 2.54/2.76 tff(9254,plain,((~r(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(9255,plain,
% 2.54/2.76 (~r(z, s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9254, 259, 9096, 9248, 9246, 95])).
% 2.54/2.76 tff(9256,plain,
% 2.54/2.76 (b(z, s(s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[293, 9255])).
% 2.54/2.76 tff(9257,plain,
% 2.54/2.76 (~b(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[7254, 9256, 9096, 259, 9118])).
% 2.54/2.76 tff(9258,plain,
% 2.54/2.76 (r(s(z), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[550, 9257])).
% 2.54/2.76 tff(9259,plain,
% 2.54/2.76 (~r(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2952, 554, 637, 95])).
% 2.54/2.76 tff(9260,plain,
% 2.54/2.76 (b(z, s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[124, 9259])).
% 2.54/2.76 tff(9261,plain,
% 2.54/2.76 (~r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9166, 637, 554, 95])).
% 2.54/2.76 tff(9262,plain,
% 2.54/2.76 (b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9192, 9261])).
% 2.54/2.76 tff(9263,plain,
% 2.54/2.76 ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9213, 171, 259, 161, 838, 1275])).
% 2.54/2.76 tff(9264,plain,
% 2.54/2.76 (~b(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9263, 9262])).
% 2.54/2.76 tff(9265,plain,
% 2.54/2.76 (r(s(s(s(z))), s(s(z)))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[2642, 9264])).
% 2.54/2.76 tff(9266,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9267,plain,
% 2.54/2.76 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9268,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.54/2.76 inference(monotonicity,[status(thm)],[9267])).
% 2.54/2.76 tff(9269,plain,
% 2.54/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.76 inference(transitivity,[status(thm)],[9268, 9266])).
% 2.54/2.76 tff(9270,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.54/2.76 inference(quant_inst,[status(thm)],[])).
% 2.54/2.76 tff(9271,plain,
% 2.54/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.76 inference(modus_ponens,[status(thm)],[9270, 9269])).
% 2.54/2.76 tff(9272,plain,
% 2.54/2.76 ($false),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9271, 106, 554, 637, 9265, 1998])).
% 2.54/2.76 tff(9273,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.76 tff(9274,plain,
% 2.54/2.76 (~r(s(z), s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9273, 838, 637, 259, 554, 9260, 1275, 95])).
% 2.54/2.76 tff(9275,plain,
% 2.54/2.76 (~r(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9166, 554, 637, 95])).
% 2.54/2.76 tff(9276,plain,
% 2.54/2.76 (b(z, s(s(s(z))))),
% 2.54/2.76 inference(unit_resolution,[status(thm)],[9192, 9275])).
% 2.54/2.76 tff(9277,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 2.54/2.76 tff(9278,plain,
% 2.54/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(z, s(s(s(z))))))),
% 2.54/2.76 inference(rewrite,[status(thm)],[])).
% 2.54/2.76 tff(9279,plain,
% 2.54/2.76 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9280,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(z, s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[9279])).
% 2.54/2.77 tff(9281,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(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(z, s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[9280, 9278])).
% 2.54/2.77 tff(9282,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9283,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9282, 9281])).
% 2.54/2.77 tff(9284,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9283, 171, 3281, 1976, 83, 838, 376, 9277])).
% 2.54/2.77 tff(9285,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9286,plain,
% 2.54/2.77 (~b(s(z), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9285, 838, 9096, 376, 9276, 83])).
% 2.54/2.77 tff(9287,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1996, 9286, 9274])).
% 2.54/2.77 tff(9288,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9289,plain,
% 2.54/2.77 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9288, 9244, 83, 9246, 259, 9258, 1275, 95])).
% 2.54/2.77 tff(9290,plain,
% 2.54/2.77 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2614, 9289])).
% 2.54/2.77 tff(9291,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8535, 9290, 502, 9116])).
% 2.54/2.77 tff(9292,plain,
% 2.54/2.77 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2842, 9291, 2264])).
% 2.54/2.77 tff(9293,plain,
% 2.54/2.77 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9195, 9290, 502, 9116])).
% 2.54/2.77 tff(9294,plain,
% 2.54/2.77 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6475, 9293])).
% 2.54/2.77 tff(9295,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9176, 9294, 9292, 9256, 9258, 95, 259, 83, 1275])).
% 2.54/2.77 tff(9296,plain,((~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9297,plain,
% 2.54/2.77 (~b(s(s(z)), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9296, 502, 83, 1275, 95])).
% 2.54/2.77 tff(9298,plain,
% 2.54/2.77 (r(s(s(z)), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[244, 9297])).
% 2.54/2.77 tff(9299,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[4675, 106, 9298, 95, 502])).
% 2.54/2.77 tff(9300,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[225, 9299])).
% 2.54/2.77 tff(9301,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5833, 106, 9298, 95, 502])).
% 2.54/2.77 tff(9302,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[205, 9301])).
% 2.54/2.77 tff(9303,plain,
% 2.54/2.77 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9224, 127, 502, 95])).
% 2.54/2.77 tff(9304,plain,
% 2.54/2.77 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[498, 9303])).
% 2.54/2.77 tff(9305,plain,
% 2.54/2.77 (~r(z, s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9205, 127, 502, 95])).
% 2.54/2.77 tff(9306,plain,
% 2.54/2.77 (b(z, s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[124, 9305])).
% 2.54/2.77 tff(9307,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5902, 171, 9306, 83, 160, 207, 9304])).
% 2.54/2.77 tff(9308,plain,((~r(s(s(s(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(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9309,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9308, 9302, 83, 9300, 502, 95])).
% 2.54/2.77 tff(9310,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[145, 9309])).
% 2.54/2.77 tff(9311,plain,
% 2.54/2.77 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8511, 9310, 1275, 83, 502])).
% 2.54/2.77 tff(9312,plain,
% 2.54/2.77 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[454, 9311, 254])).
% 2.54/2.77 tff(9313,plain,
% 2.54/2.77 (~b(s(z), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8497, 171, 1275, 9302, 9300])).
% 2.54/2.77 tff(9314,plain,
% 2.54/2.77 (r(s(z), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[550, 9313])).
% 2.54/2.77 tff(9315,plain,
% 2.54/2.77 (~b(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[6431, 9312, 9096, 83, 9302, 9310])).
% 2.54/2.77 tff(9316,plain,
% 2.54/2.77 (r(s(s(z)), z)),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[157, 9315])).
% 2.54/2.77 tff(9317,plain,
% 2.54/2.77 (~r(z, s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[5959, 9316, 9314, 95])).
% 2.54/2.77 tff(9318,plain,
% 2.54/2.77 (b(z, s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[498, 9317])).
% 2.54/2.77 tff(9319,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8596, 9318, 1275, 502, 9310, 9118, 9312, 9116])).
% 2.54/2.77 tff(9320,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1368, 9319])).
% 2.54/2.77 tff(9321,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9322,plain,
% 2.54/2.77 (((~r(s(z), s(s(z)))) | (~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(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9323,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[9322])).
% 2.54/2.77 tff(9324,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[9323, 9321])).
% 2.54/2.77 tff(9325,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9326,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9325, 9324])).
% 2.54/2.77 tff(9327,plain,
% 2.54/2.77 (~r(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9326, 106, 554, 2, 747])).
% 2.54/2.77 tff(9328,plain,
% 2.54/2.77 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[979, 25, 9327])).
% 2.54/2.77 tff(9329,plain,
% 2.54/2.77 (b(s(s(z)), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9328, 900])).
% 2.54/2.77 tff(9330,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~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)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9331,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9332,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~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))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9331, 9330])).
% 2.54/2.77 tff(9333,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9332, 106, 554, 2, 502])).
% 2.54/2.77 tff(9334,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[225, 9333])).
% 2.54/2.77 tff(9335,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9336,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9337,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9336, 9335])).
% 2.54/2.77 tff(9338,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9337, 106, 554, 502, 747])).
% 2.54/2.77 tff(9339,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1368, 9338])).
% 2.54/2.77 tff(9340,plain,
% 2.54/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9341,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9342,plain,
% 2.54/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9341, 9340])).
% 2.54/2.77 tff(9343,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9342, 106, 554, 2, 747])).
% 2.54/2.77 tff(9344,plain,
% 2.54/2.77 (b(s(s(s(z))), s(s(z)))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2640, 25, 9343, 80])).
% 2.54/2.77 tff(9345,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9346,plain,
% 2.54/2.77 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9347,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[9346])).
% 2.54/2.77 tff(9348,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[9347, 9345])).
% 2.54/2.77 tff(9349,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.77 inference(quant_inst,[status(thm)],[])).
% 2.54/2.77 tff(9350,plain,
% 2.54/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.54/2.77 inference(modus_ponens,[status(thm)],[9349, 9348])).
% 2.54/2.77 tff(9351,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9350, 171, 9344, 9339, 9334, 9329])).
% 2.54/2.77 tff(9352,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9353,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9352, 9314, 9298, 502])).
% 2.54/2.77 tff(9354,plain,
% 2.54/2.77 (b(s(s(s(z))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[1173, 9353])).
% 2.54/2.77 tff(9355,plain,
% 2.54/2.77 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8545, 9312, 9118, 9354])).
% 2.54/2.77 tff(9356,plain,
% 2.54/2.77 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2842, 9355, 2264])).
% 2.54/2.77 tff(9357,plain,
% 2.54/2.77 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8535, 9356, 502, 9116])).
% 2.54/2.77 tff(9358,plain,
% 2.54/2.77 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[2614, 9357])).
% 2.54/2.77 tff(9359,plain,
% 2.54/2.77 ($false),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[8606, 171, 9354, 9358, 1275, 9320])).
% 2.54/2.77 tff(9360,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.77 tff(9361,plain,
% 2.54/2.77 (~r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[9360, 83, 95, 1275])).
% 2.54/2.77 tff(9362,plain,
% 2.54/2.77 (b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.77 inference(unit_resolution,[status(thm)],[479, 9361])).
% 2.54/2.77 tff(9363,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9364,plain,
% 2.54/2.77 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(rewrite,[status(thm)],[])).
% 2.54/2.77 tff(9365,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.54/2.77 inference(monotonicity,[status(thm)],[9364])).
% 2.54/2.77 tff(9366,plain,
% 2.54/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.77 inference(transitivity,[status(thm)],[9365, 9363])).
% 2.54/2.78 tff(9367,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9368,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9367, 9366])).
% 2.54/2.78 tff(9369,plain,
% 2.54/2.78 ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9368, 171, 9096, 83, 1275])).
% 2.54/2.78 tff(9370,plain,
% 2.54/2.78 (~b(z, s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9369, 9362])).
% 2.54/2.78 tff(9371,plain,
% 2.54/2.78 (r(z, s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[498, 9370])).
% 2.54/2.78 tff(9372,plain,
% 2.54/2.78 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8053, 9362, 1275, 83])).
% 2.54/2.78 tff(9373,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[321, 9372, 255])).
% 2.54/2.78 tff(9374,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9375,plain,
% 2.54/2.78 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9376,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[9375])).
% 2.54/2.78 tff(9377,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.78 inference(transitivity,[status(thm)],[9376, 9374])).
% 2.54/2.78 tff(9378,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9379,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9378, 9377])).
% 2.54/2.78 tff(9380,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9379, 171, 9096, 1275, 9362])).
% 2.54/2.78 tff(9381,plain,
% 2.54/2.78 (r(s(s(s(s(s(z))))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[145, 9380])).
% 2.54/2.78 tff(9382,plain,
% 2.54/2.78 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[7029, 106, 2, 95, 9373])).
% 2.54/2.78 tff(9383,plain,
% 2.54/2.78 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[351, 9382])).
% 2.54/2.78 tff(9384,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5719, 3686, 95, 83, 9362, 2, 323])).
% 2.54/2.78 tff(9385,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[205, 9384])).
% 2.54/2.78 tff(9386,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6149, 2, 95, 9373])).
% 2.54/2.78 tff(9387,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[374, 9386, 355])).
% 2.54/2.78 tff(9388,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9389,plain,
% 2.54/2.78 (((~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(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(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)))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9390,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[9389])).
% 2.54/2.78 tff(9391,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[9390, 9388])).
% 2.54/2.78 tff(9392,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9393,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9392, 9391])).
% 2.54/2.78 tff(9394,plain,
% 2.54/2.78 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9393, 171, 83, 9387, 9383])).
% 2.54/2.78 tff(9395,plain,
% 2.54/2.78 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[225, 9394])).
% 2.54/2.78 tff(9396,plain,
% 2.54/2.78 (((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9397,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[9396])).
% 2.54/2.78 tff(9398,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[9397, 8675])).
% 2.54/2.78 tff(9399,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9400,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9399, 9398])).
% 2.54/2.78 tff(9401,plain,
% 2.54/2.78 (~r(z, s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9400, 106, 9395, 9371, 9385])).
% 2.54/2.78 tff(9402,plain,
% 2.54/2.78 (b(z, s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[124, 9401])).
% 2.54/2.78 tff(9403,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9404,plain,
% 2.54/2.78 (((~b(s(s(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(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9405,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[9404])).
% 2.54/2.78 tff(9406,plain,
% 2.54/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[9405, 9403])).
% 2.54/2.78 tff(9407,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9408,plain,
% 2.54/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9407, 9406])).
% 2.54/2.78 tff(9409,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9408, 171, 323, 9096, 9402, 3686, 1275, 9383])).
% 2.54/2.78 tff(9410,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(9411,plain,
% 2.54/2.78 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9410, 323, 1275, 83, 2, 95])).
% 2.54/2.78 tff(9412,plain,
% 2.54/2.78 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[3668, 9411])).
% 2.54/2.78 tff(9413,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9414,plain,
% 2.54/2.78 (((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~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(z, s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9415,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.54/2.78 inference(monotonicity,[status(thm)],[9414])).
% 2.54/2.78 tff(9416,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.54/2.78 inference(transitivity,[status(thm)],[9415, 9413])).
% 2.54/2.78 tff(9417,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9418,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9417, 9416])).
% 2.54/2.78 tff(9419,plain,
% 2.54/2.78 (~r(s(s(s(s(z)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9418, 106, 9412, 9381, 9371])).
% 2.54/2.78 tff(9420,plain,
% 2.54/2.78 (b(s(s(s(s(z)))), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[274, 9419])).
% 2.54/2.78 tff(9421,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9422,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.78 inference(quant_inst,[status(thm)],[])).
% 2.54/2.78 tff(9423,plain,
% 2.54/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.54/2.78 inference(modus_ponens,[status(thm)],[9422, 9421])).
% 2.54/2.78 tff(9424,plain,
% 2.54/2.78 (~r(z, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9423, 106, 9412, 9381, 9371])).
% 2.54/2.78 tff(9425,plain,
% 2.54/2.78 (b(z, s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[293, 9424])).
% 2.54/2.78 tff(9426,plain,
% 2.54/2.78 (~b(s(s(z)), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[2535, 9425, 9387, 9420])).
% 2.54/2.78 tff(9427,plain,
% 2.54/2.78 (r(s(s(z)), z)),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[157, 9426])).
% 2.54/2.78 tff(9428,plain,
% 2.54/2.78 (~r(z, s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[6001, 9427, 95, 2])).
% 2.54/2.78 tff(9429,plain,
% 2.54/2.78 (b(z, s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[124, 9428])).
% 2.54/2.78 tff(9430,plain,
% 2.54/2.78 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5981, 9429, 9387, 9425])).
% 2.54/2.78 tff(9431,plain,
% 2.54/2.78 (r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[351, 9430])).
% 2.54/2.78 tff(9432,plain,
% 2.54/2.78 (~r(s(z), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[5971, 9431, 9412, 2])).
% 2.54/2.78 tff(9433,plain,
% 2.54/2.78 (b(s(z), s(s(s(s(z)))))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[454, 9432, 254])).
% 2.54/2.78 tff(9434,plain,
% 2.54/2.78 ($false),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[8157, 171, 323, 9429, 83, 9362, 9433, 9420])).
% 2.54/2.78 tff(9435,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.78 tff(9436,plain,
% 2.54/2.78 (~b(s(z), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[9435, 2, 83, 95, 1275])).
% 2.54/2.78 tff(9437,plain,
% 2.54/2.78 (r(s(z), s(s(z)))),
% 2.54/2.78 inference(unit_resolution,[status(thm)],[550, 9436])).
% 2.54/2.78 tff(9438,plain,
% 2.54/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.78 inference(rewrite,[status(thm)],[])).
% 2.54/2.78 tff(9439,plain,
% 2.54/2.78 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9440,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9439])).
% 2.54/2.79 tff(9441,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9440, 9438])).
% 2.54/2.79 tff(9442,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9443,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9442, 9441])).
% 2.54/2.79 tff(9444,plain,
% 2.54/2.79 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9443, 106, 554, 2, 263])).
% 2.54/2.79 tff(9445,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[351, 9444])).
% 2.54/2.79 tff(9446,plain,
% 2.54/2.79 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6149, 2, 95, 263])).
% 2.54/2.79 tff(9447,plain,
% 2.54/2.79 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[374, 9446, 355])).
% 2.54/2.79 tff(9448,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9449,plain,
% 2.54/2.79 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, 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)))), z)))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9450,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9449])).
% 2.54/2.79 tff(9451,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9450, 9448])).
% 2.54/2.79 tff(9452,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9453,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9452, 9451])).
% 2.54/2.79 tff(9454,plain,
% 2.54/2.79 (~b(s(s(s(s(z)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9453, 171, 161, 9447, 9445])).
% 2.54/2.79 tff(9455,plain,
% 2.54/2.79 (r(s(s(s(s(z)))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[274, 9454])).
% 2.54/2.79 tff(9456,plain,
% 2.54/2.79 (~b(z, s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5981, 9445, 9447, 161])).
% 2.54/2.79 tff(9457,plain,
% 2.54/2.79 (r(z, s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[293, 9456])).
% 2.54/2.79 tff(9458,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9459,plain,
% 2.54/2.79 (((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9460,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9459])).
% 2.54/2.79 tff(9461,plain,
% 2.54/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9460, 9458])).
% 2.54/2.79 tff(9462,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9463,plain,
% 2.54/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9462, 9461])).
% 2.54/2.79 tff(9464,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9463, 106, 95, 9457, 263, 9455])).
% 2.54/2.79 tff(9465,plain,((~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9466,plain,
% 2.54/2.79 (~b(z, s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9465, 9437, 9373, 95, 2])).
% 2.54/2.79 tff(9467,plain,
% 2.54/2.79 (r(z, s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[124, 9466])).
% 2.54/2.79 tff(9468,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5916, 106, 9437, 2, 95, 9467])).
% 2.54/2.79 tff(9469,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9470,plain,
% 2.54/2.79 (~r(s(s(z)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9469, 83, 95, 1275])).
% 2.54/2.79 tff(9471,plain,
% 2.54/2.79 (b(s(s(z)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[244, 9470])).
% 2.54/2.79 tff(9472,plain,
% 2.54/2.79 (~r(z, s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[8101, 9471, 83, 1275, 9362, 9381])).
% 2.54/2.79 tff(9473,plain,
% 2.54/2.79 (b(z, s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[124, 9472])).
% 2.54/2.79 tff(9474,plain,
% 2.54/2.79 (~b(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[7045, 9473, 9096, 9471])).
% 2.54/2.79 tff(9475,plain,
% 2.54/2.79 (r(s(z), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[550, 9474])).
% 2.54/2.79 tff(9476,plain,
% 2.54/2.79 (~r(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[5959, 9475, 9371, 95])).
% 2.54/2.79 tff(9477,plain,
% 2.54/2.79 (b(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[157, 9476])).
% 2.54/2.79 tff(9478,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9479,plain,
% 2.54/2.79 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9480,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9479])).
% 2.54/2.79 tff(9481,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9480, 9478])).
% 2.54/2.79 tff(9482,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9483,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9482, 9481])).
% 2.54/2.79 tff(9484,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9483, 171, 9096, 9471, 9477, 1275, 9362])).
% 2.54/2.79 tff(9485,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9486,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9485, 8041, 31])).
% 2.54/2.79 tff(9487,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[427, 9486])).
% 2.54/2.79 tff(9488,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9379, 171, 3281, 1275, 4, 159])).
% 2.54/2.79 tff(9489,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9490,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9489, 4, 1275, 9096])).
% 2.54/2.79 tff(9491,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[145, 9490])).
% 2.54/2.79 tff(9492,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9485, 1275, 95])).
% 2.54/2.79 tff(9493,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[427, 9492])).
% 2.54/2.79 tff(9494,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9495,plain,
% 2.54/2.79 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(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))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9496,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(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)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9495])).
% 2.54/2.79 tff(9497,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9496, 9494])).
% 2.54/2.79 tff(9498,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9499,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(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)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9498, 9497])).
% 2.54/2.79 tff(9500,plain,
% 2.54/2.79 (~b(z, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9499, 171, 9096, 1275, 4])).
% 2.54/2.79 tff(9501,plain,
% 2.54/2.79 (r(z, s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[498, 9500])).
% 2.54/2.79 tff(9502,plain,
% 2.54/2.79 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9002, 9501, 9493, 600])).
% 2.54/2.79 tff(9503,plain,
% 2.54/2.79 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[205, 9502])).
% 2.54/2.79 tff(9504,plain,
% 2.54/2.79 (~b(s(s(z)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[3673, 9503, 323, 4])).
% 2.54/2.79 tff(9505,plain,
% 2.54/2.79 (r(s(s(z)), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[244, 9504])).
% 2.54/2.79 tff(9506,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9379, 171, 3281, 1275, 4])).
% 2.54/2.79 tff(9507,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[143, 25, 140, 9506])).
% 2.54/2.79 tff(9508,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9509,plain,
% 2.54/2.79 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(rewrite,[status(thm)],[])).
% 2.54/2.79 tff(9510,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.54/2.79 inference(monotonicity,[status(thm)],[9509])).
% 2.54/2.79 tff(9511,plain,
% 2.54/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.54/2.79 inference(transitivity,[status(thm)],[9510, 9508])).
% 2.54/2.79 tff(9512,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.54/2.79 inference(quant_inst,[status(thm)],[])).
% 2.54/2.79 tff(9513,plain,
% 2.54/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.54/2.79 inference(modus_ponens,[status(thm)],[9512, 9511])).
% 2.54/2.79 tff(9514,plain,
% 2.54/2.79 ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9513, 171, 323, 3281, 1, 4])).
% 2.54/2.79 tff(9515,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9514, 1275])).
% 2.54/2.79 tff(9516,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[225, 9515])).
% 2.54/2.79 tff(9517,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6027, 106, 2, 600, 9516, 9507])).
% 2.54/2.79 tff(9518,plain,((~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9519,plain,
% 2.54/2.79 (~b(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9518, 9505, 1275, 9096, 323, 600, 4])).
% 2.54/2.79 tff(9520,plain,
% 2.54/2.79 (~r(s(s(z)), z)),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[6001, 9505, 95, 600])).
% 2.54/2.79 tff(9521,plain,
% 2.54/2.79 ($false),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[157, 9520, 9519])).
% 2.54/2.79 tff(9522,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.79 tff(9523,plain,
% 2.54/2.79 (~b(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[9522, 600, 95, 1275, 323])).
% 2.54/2.79 tff(9524,plain,
% 2.54/2.79 (r(s(s(s(s(s(z))))), s(z))),
% 2.54/2.79 inference(unit_resolution,[status(thm)],[479, 9523])).
% 2.54/2.80 tff(9525,plain,
% 2.54/2.80 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[6123, 2, 95, 3281, 600, 323])).
% 2.54/2.80 tff(9526,plain,
% 2.54/2.80 (b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[374, 9525, 355])).
% 2.54/2.80 tff(9527,plain,
% 2.54/2.80 (~b(s(s(s(s(z)))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5851, 9526, 95, 323, 502, 2])).
% 2.54/2.80 tff(9528,plain,
% 2.54/2.80 (r(s(s(s(s(z)))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[321, 9527, 255])).
% 2.54/2.80 tff(9529,plain,
% 2.54/2.80 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5552, 9528, 502, 95])).
% 2.54/2.80 tff(9530,plain,
% 2.54/2.80 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[3668, 9529])).
% 2.54/2.80 tff(9531,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[5760, 4677, 5835, 9526, 9530])).
% 2.54/2.80 tff(9532,plain,((~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(9533,plain,
% 2.54/2.80 (~r(s(s(z)), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[9532, 9524, 95, 323, 9096, 600])).
% 2.54/2.80 tff(9534,plain,
% 2.54/2.80 (b(s(s(z)), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[244, 9533])).
% 2.54/2.80 tff(9535,plain,
% 2.54/2.80 (~b(s(s(z)), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[6237, 9534, 9096, 323])).
% 2.54/2.80 tff(9536,plain,
% 2.54/2.80 (r(s(s(z)), z)),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[157, 9535])).
% 2.54/2.80 tff(9537,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[1317, 106, 95, 5609, 502, 263])).
% 2.54/2.80 tff(9538,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(9539,plain,
% 2.54/2.80 (~r(s(s(s(s(z)))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[9538, 9524, 9493, 95])).
% 2.54/2.80 tff(9540,plain,
% 2.54/2.80 (b(s(s(s(s(z)))), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[321, 9539, 255])).
% 2.54/2.80 tff(9541,plain,
% 2.54/2.80 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[365, 9540, 323, 9534])).
% 2.54/2.80 tff(9542,plain,
% 2.54/2.80 (r(s(s(s(s(z)))), s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[374, 9541, 355])).
% 2.54/2.80 tff(9543,plain,
% 2.54/2.80 (~b(z, s(s(s(s(z)))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[7254, 9540, 9096, 323, 9534])).
% 2.54/2.80 tff(9544,plain,
% 2.54/2.80 (r(z, s(s(s(s(z)))))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[293, 9543])).
% 2.54/2.80 tff(9545,plain,
% 2.54/2.80 ($false),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[6247, 9544, 9542, 600, 9536])).
% 2.54/2.80 tff(9546,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.54/2.80 tff(9547,plain,
% 2.54/2.80 (~r(z, s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[9546, 323, 95, 1275])).
% 2.54/2.80 tff(9548,plain,
% 2.54/2.80 (b(z, s(s(z)))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[124, 9547])).
% 2.54/2.80 tff(9549,plain,
% 2.54/2.80 (~b(s(s(z)), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[7045, 9548, 9096, 323])).
% 2.54/2.80 tff(9550,plain,
% 2.54/2.80 (r(s(s(z)), s(z))),
% 2.54/2.80 inference(unit_resolution,[status(thm)],[244, 9549])).
% 2.64/2.80 tff(9551,plain,
% 2.64/2.80 (~b(s(s(s(s(s(z))))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9379, 171, 9096, 1275, 4])).
% 2.64/2.80 tff(9552,plain,
% 2.64/2.80 (r(s(s(s(s(s(z))))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[145, 9551])).
% 2.64/2.80 tff(9553,plain,
% 2.64/2.80 (~b(z, s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5981, 2352, 161, 356])).
% 2.64/2.80 tff(9554,plain,
% 2.64/2.80 (r(z, s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[293, 9553])).
% 2.64/2.80 tff(9555,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9556,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(9557,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[9556, 9555])).
% 2.64/2.80 tff(9558,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9557, 106, 5609, 5567, 127, 2118])).
% 2.64/2.80 tff(9559,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(9560,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9559, 9554, 5609, 127])).
% 2.64/2.80 tff(9561,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[274, 9560])).
% 2.64/2.80 tff(9562,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9453, 171, 161, 356, 2352, 9561])).
% 2.64/2.80 tff(9563,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(9564,plain,
% 2.64/2.80 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9563, 8069, 161, 5609, 127])).
% 2.64/2.80 tff(9565,plain,
% 2.64/2.80 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[351, 9564])).
% 2.64/2.80 tff(9566,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[7029, 106, 2, 95, 263, 9565])).
% 2.64/2.80 tff(9567,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(9568,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9567, 9552, 95, 9548, 9493, 9550])).
% 2.64/2.80 tff(9569,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[321, 9568, 255])).
% 2.64/2.80 tff(9570,plain,
% 2.64/2.80 (~b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8704, 357, 1275, 3686])).
% 2.64/2.80 tff(9571,plain,
% 2.64/2.80 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[479, 9570])).
% 2.64/2.80 tff(9572,plain,
% 2.64/2.80 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8331, 357, 1275, 3686])).
% 2.64/2.80 tff(9573,plain,
% 2.64/2.80 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[427, 9572])).
% 2.64/2.80 tff(9574,plain,
% 2.64/2.80 (~b(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[5892, 171, 3281, 376, 357])).
% 2.64/2.80 tff(9575,plain,
% 2.64/2.80 (r(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[272, 25, 52, 9574])).
% 2.64/2.80 tff(9576,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), 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)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9577,plain,
% 2.64/2.80 (((~r(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)))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), 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)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9578,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), 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))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[9577])).
% 2.64/2.80 tff(9579,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), 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)))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[9578, 9576])).
% 2.64/2.80 tff(9580,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(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)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(9581,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), 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))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[9580, 9579])).
% 2.64/2.80 tff(9582,plain,
% 2.64/2.80 (~r(z, s(s(s(s(s(z))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9581, 106, 9573, 6195, 9575])).
% 2.64/2.80 tff(9583,plain,
% 2.64/2.80 (b(z, s(s(s(s(s(z))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[498, 9582])).
% 2.64/2.80 tff(9584,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9585,plain,
% 2.64/2.80 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(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)))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9586,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[9585])).
% 2.64/2.80 tff(9587,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[9586, 9584])).
% 2.64/2.80 tff(9588,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(9589,plain,
% 2.64/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[9588, 9587])).
% 2.64/2.80 tff(9590,plain,
% 2.64/2.80 (~r(s(s(s(s(s(z))))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9589, 106, 9573, 6195, 9575])).
% 2.64/2.80 tff(9591,plain,
% 2.64/2.80 (b(s(s(s(s(s(z))))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[145, 9590])).
% 2.64/2.80 tff(9592,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8932, 9591, 9583, 1275, 357, 3686])).
% 2.64/2.80 tff(9593,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(9594,plain,
% 2.64/2.80 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9593, 357, 1275, 3686, 3281])).
% 2.64/2.80 tff(9595,plain,
% 2.64/2.80 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[454, 9594, 254])).
% 2.64/2.80 tff(9596,plain,
% 2.64/2.80 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[6821, 9595, 9573, 9571])).
% 2.64/2.80 tff(9597,plain,
% 2.64/2.80 (b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[374, 9596, 355])).
% 2.64/2.80 tff(9598,plain,
% 2.64/2.80 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[8468, 2, 3, 502])).
% 2.64/2.80 tff(9599,plain,
% 2.64/2.80 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[225, 9598])).
% 2.64/2.80 tff(9600,plain,
% 2.64/2.80 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[203, 25, 5834, 198])).
% 2.64/2.80 tff(9601,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9602,plain,
% 2.64/2.80 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9603,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[9602])).
% 2.64/2.80 tff(9604,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(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(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.80 inference(transitivity,[status(thm)],[9603, 9601])).
% 2.64/2.80 tff(9605,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(9606,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[9605, 9604])).
% 2.64/2.80 tff(9607,plain,
% 2.64/2.80 ($false),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9606, 171, 3686, 1275, 9600, 9599, 357])).
% 2.64/2.80 tff(9608,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.80 tff(9609,plain,
% 2.64/2.80 (~r(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9608, 3, 1275, 3686, 357, 9571, 2])).
% 2.64/2.80 tff(9610,plain,
% 2.64/2.80 (b(s(z), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[30, 9609])).
% 2.64/2.80 tff(9611,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9612,plain,
% 2.64/2.80 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9613,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[9612])).
% 2.64/2.80 tff(9614,plain,
% 2.64/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(transitivity,[status(thm)],[9613, 9611])).
% 2.64/2.80 tff(9615,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.80 inference(quant_inst,[status(thm)],[])).
% 2.64/2.80 tff(9616,plain,
% 2.64/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.64/2.80 inference(modus_ponens,[status(thm)],[9615, 9614])).
% 2.64/2.80 tff(9617,plain,
% 2.64/2.80 (~b(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[9616, 171, 3281, 9610, 357])).
% 2.64/2.80 tff(9618,plain,
% 2.64/2.80 (r(s(s(s(s(z)))), z)),
% 2.64/2.80 inference(unit_resolution,[status(thm)],[272, 25, 52, 9617])).
% 2.64/2.80 tff(9619,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9620,plain,
% 2.64/2.80 (((~r(s(s(s(s(z)))), z)) | (~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(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.80 inference(rewrite,[status(thm)],[])).
% 2.64/2.80 tff(9621,plain,
% 2.64/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.80 inference(monotonicity,[status(thm)],[9620])).
% 2.64/2.80 tff(9622,plain,
% 2.64/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[9621, 9619])).
% 2.64/2.81 tff(9623,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(9624,plain,
% 2.64/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[9623, 9622])).
% 2.64/2.81 tff(9625,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9624, 106, 9573, 9571, 3, 9618])).
% 2.64/2.81 tff(9626,plain,((~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9627,plain,
% 2.64/2.81 (~r(s(s(z)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9626, 9595, 357, 1275, 3686, 3281])).
% 2.64/2.81 tff(9628,plain,
% 2.64/2.81 (b(s(s(z)), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[244, 9627])).
% 2.64/2.81 tff(9629,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9630,plain,
% 2.64/2.81 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9631,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[9630])).
% 2.64/2.81 tff(9632,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[9631, 9629])).
% 2.64/2.81 tff(9633,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(9634,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[9633, 9632])).
% 2.64/2.81 tff(9635,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9634, 171, 3281, 259, 3133, 357, 356])).
% 2.64/2.81 tff(9636,plain,((~b(s(z), z)) | (~b(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))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9637,plain,
% 2.64/2.81 (~b(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9636, 9628, 3281, 357, 9597])).
% 2.64/2.81 tff(9638,plain,
% 2.64/2.81 (r(s(z), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[30, 9637])).
% 2.64/2.81 tff(9639,plain,
% 2.64/2.81 (~b(s(z), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[365, 9628, 357, 9597])).
% 2.64/2.81 tff(9640,plain,
% 2.64/2.81 (r(s(z), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[550, 9639])).
% 2.64/2.81 tff(9641,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5575, 5567, 95, 554])).
% 2.64/2.81 tff(9642,plain,
% 2.64/2.81 (b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[157, 9641])).
% 2.64/2.81 tff(9643,plain,
% 2.64/2.81 (b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[349, 25, 346, 7179])).
% 2.64/2.81 tff(9644,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(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(z), s(s(s(s(s(z))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9645,plain,
% 2.64/2.81 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, 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(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9646,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(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(z), s(s(s(s(s(z)))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[9645])).
% 2.64/2.81 tff(9647,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(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(z), s(s(s(s(s(z))))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[9646, 9644])).
% 2.64/2.81 tff(9648,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(9649,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[9648, 9647])).
% 2.64/2.81 tff(9650,plain,
% 2.64/2.81 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9649, 171, 3281, 1, 3686, 1275])).
% 2.64/2.81 tff(9651,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9650, 9643])).
% 2.64/2.81 tff(9652,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[272, 25, 52, 9651])).
% 2.64/2.81 tff(9653,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7122, 106, 95, 600, 3, 9652])).
% 2.64/2.81 tff(9654,plain,((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9655,plain,
% 2.64/2.81 (~r(z, s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9654, 9642, 3, 3281, 95, 3686, 1275, 554])).
% 2.64/2.81 tff(9656,plain,
% 2.64/2.81 (b(z, s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[124, 9655])).
% 2.64/2.81 tff(9657,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6307, 9656, 259, 9642, 356])).
% 2.64/2.81 tff(9658,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[274, 9657])).
% 2.64/2.81 tff(9659,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6315, 106, 95, 5567, 3, 9658])).
% 2.64/2.81 tff(9660,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9661,plain,
% 2.64/2.81 (~r(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9660, 9638, 9595, 9628, 9597, 3281, 3686, 1275, 9640])).
% 2.64/2.81 tff(9662,plain,
% 2.64/2.81 (b(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[293, 9661])).
% 2.64/2.81 tff(9663,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9664,plain,
% 2.64/2.81 (((~b(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(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(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9665,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[9664])).
% 2.64/2.81 tff(9666,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[9665, 9663])).
% 2.64/2.81 tff(9667,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(9668,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[9667, 9666])).
% 2.64/2.81 tff(9669,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9668, 171, 259, 161, 3686, 1275, 356, 2527])).
% 2.64/2.81 tff(9670,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9671,plain,
% 2.64/2.81 (~b(z, s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9670, 9628, 3686, 1275, 9597, 9662])).
% 2.64/2.81 tff(9672,plain,
% 2.64/2.81 (r(z, s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[124, 9671])).
% 2.64/2.81 tff(9673,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2952, 9672, 9640, 9638])).
% 2.64/2.81 tff(9674,plain,
% 2.64/2.81 (~b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9654, 9672, 9595, 3281, 9638, 3686, 1275, 9640])).
% 2.64/2.81 tff(9675,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[157, 9674, 9673])).
% 2.64/2.81 tff(9676,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9677,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9676, 9569, 1275, 9096])).
% 2.64/2.81 tff(9678,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3668, 9677])).
% 2.64/2.81 tff(9679,plain,
% 2.64/2.81 (~r(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5649, 9678, 9493, 9552])).
% 2.64/2.81 tff(9680,plain,
% 2.64/2.81 (b(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[293, 9679])).
% 2.64/2.81 tff(9681,plain,
% 2.64/2.81 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7938, 9680, 9096, 323, 9569])).
% 2.64/2.81 tff(9682,plain,
% 2.64/2.81 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[454, 9681, 254])).
% 2.64/2.81 tff(9683,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8762, 9678, 9493, 9501])).
% 2.64/2.81 tff(9684,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2614, 9683])).
% 2.64/2.81 tff(9685,plain,
% 2.64/2.81 (~b(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[8778, 171, 9684, 1275, 4])).
% 2.64/2.81 tff(9686,plain,
% 2.64/2.81 (r(s(z), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1996, 9685])).
% 2.64/2.81 tff(9687,plain,
% 2.64/2.81 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2836, 9686, 9678, 9682])).
% 2.64/2.81 tff(9688,plain,
% 2.64/2.81 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[2842, 9687, 2264])).
% 2.64/2.81 tff(9689,plain,
% 2.64/2.81 (~b(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9041, 171, 323, 9684, 1275, 4])).
% 2.64/2.81 tff(9690,plain,
% 2.64/2.81 (r(s(s(s(z))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[1173, 9689])).
% 2.64/2.81 tff(9691,plain,
% 2.64/2.81 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9141, 9686, 9682, 9690])).
% 2.64/2.81 tff(9692,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[6475, 9691])).
% 2.64/2.81 tff(9693,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9694,plain,
% 2.64/2.81 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(rewrite,[status(thm)],[])).
% 2.64/2.81 tff(9695,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 2.64/2.81 inference(monotonicity,[status(thm)],[9694])).
% 2.64/2.81 tff(9696,plain,
% 2.64/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(transitivity,[status(thm)],[9695, 9693])).
% 2.64/2.81 tff(9697,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.81 inference(quant_inst,[status(thm)],[])).
% 2.64/2.81 tff(9698,plain,
% 2.64/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 2.64/2.81 inference(modus_ponens,[status(thm)],[9697, 9696])).
% 2.64/2.81 tff(9699,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9698, 171, 838, 6462, 2852, 2527, 9277])).
% 2.64/2.81 tff(9700,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9701,plain,
% 2.64/2.81 (~b(z, s(s(s(z))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9700, 9692, 9684, 9680, 9688])).
% 2.64/2.81 tff(9702,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9059, 9701, 9692, 95, 9680, 9690, 9688])).
% 2.64/2.81 tff(9703,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.81 tff(9704,plain,
% 2.64/2.81 (~b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9703, 323, 1275, 95])).
% 2.64/2.81 tff(9705,plain,
% 2.64/2.81 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[479, 9704])).
% 2.64/2.81 tff(9706,plain,
% 2.64/2.81 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9538, 9705, 9493, 95])).
% 2.64/2.81 tff(9707,plain,
% 2.64/2.81 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[321, 9706, 255])).
% 2.64/2.81 tff(9708,plain,
% 2.64/2.81 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[9676, 9707, 1275, 9096])).
% 2.64/2.81 tff(9709,plain,
% 2.64/2.81 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[3668, 9708])).
% 2.64/2.81 tff(9710,plain,
% 2.64/2.81 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7068, 9709, 9493, 9705])).
% 2.64/2.81 tff(9711,plain,
% 2.64/2.81 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[454, 9710, 254])).
% 2.64/2.81 tff(9712,plain,
% 2.64/2.81 (~b(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7938, 9711, 9096, 323, 9707])).
% 2.64/2.81 tff(9713,plain,
% 2.64/2.81 (r(z, s(s(s(s(z)))))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[293, 9712])).
% 2.64/2.81 tff(9714,plain,
% 2.64/2.81 (~r(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[7309, 9713, 9550, 95])).
% 2.64/2.81 tff(9715,plain,
% 2.64/2.81 (b(s(s(z)), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[157, 9714])).
% 2.64/2.81 tff(9716,plain,
% 2.64/2.81 (~r(s(s(s(s(s(z))))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[5649, 9713, 9493, 9709])).
% 2.64/2.81 tff(9717,plain,
% 2.64/2.81 (b(s(s(s(s(s(z))))), z)),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[145, 9716])).
% 2.64/2.81 tff(9718,plain,
% 2.64/2.81 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[215, 9717, 9548, 9715])).
% 2.64/2.81 tff(9719,plain,
% 2.64/2.81 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[225, 9718])).
% 2.64/2.81 tff(9720,plain,
% 2.64/2.81 ($false),
% 2.64/2.81 inference(unit_resolution,[status(thm)],[4675, 106, 9550, 95, 9705, 9719])).
% 2.64/2.82 tff(9721,plain,((~b(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9722,plain,
% 2.64/2.82 (~b(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9721, 95, 1275])).
% 2.64/2.82 tff(9723,plain,
% 2.64/2.82 (r(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[550, 9722])).
% 2.64/2.82 tff(9724,plain,
% 2.64/2.82 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6419, 600, 95, 9723])).
% 2.64/2.82 tff(9725,plain,
% 2.64/2.82 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[205, 9724])).
% 2.64/2.82 tff(9726,plain,
% 2.64/2.82 (~r(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2952, 600, 9723, 95])).
% 2.64/2.82 tff(9727,plain,
% 2.64/2.82 (b(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[157, 9726])).
% 2.64/2.82 tff(9728,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9538, 502, 9493, 95])).
% 2.64/2.82 tff(9729,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[321, 9728, 255])).
% 2.64/2.82 tff(9730,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9676, 9729, 1275, 9096])).
% 2.64/2.82 tff(9731,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3668, 9730])).
% 2.64/2.82 tff(9732,plain,
% 2.64/2.82 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7100, 9729, 9096, 259, 1])).
% 2.64/2.82 tff(9733,plain,
% 2.64/2.82 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[454, 9732, 254])).
% 2.64/2.82 tff(9734,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7068, 9733, 9731, 9493, 502])).
% 2.64/2.82 tff(9735,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9736,plain,
% 2.64/2.82 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9735, 9727, 259, 1275, 95])).
% 2.64/2.82 tff(9737,plain,
% 2.64/2.82 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[479, 9736])).
% 2.64/2.82 tff(9738,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8650, 171, 259, 1275, 9737, 9725])).
% 2.64/2.82 tff(9739,plain,((~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9740,plain,
% 2.64/2.82 (~r(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9739, 259, 1275, 95])).
% 2.64/2.82 tff(9741,plain,
% 2.64/2.82 (b(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[124, 9740])).
% 2.64/2.82 tff(9742,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9743,plain,
% 2.64/2.82 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9744,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[9743])).
% 2.64/2.82 tff(9745,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[9744, 9742])).
% 2.64/2.82 tff(9746,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(9747,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[9746, 9745])).
% 2.64/2.82 tff(9748,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9747, 171, 3281, 259, 161, 1275, 4])).
% 2.64/2.82 tff(9749,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9750,plain,
% 2.64/2.82 (~b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9749, 259, 9096, 9741, 1275])).
% 2.64/2.82 tff(9751,plain,
% 2.64/2.82 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[479, 9750])).
% 2.64/2.82 tff(9752,plain,
% 2.64/2.82 (~b(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9735, 9751, 259, 1275, 95])).
% 2.64/2.82 tff(9753,plain,
% 2.64/2.82 (r(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[157, 9752])).
% 2.64/2.82 tff(9754,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9538, 9751, 9493, 95])).
% 2.64/2.82 tff(9755,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[321, 9754, 255])).
% 2.64/2.82 tff(9756,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9676, 9755, 1275, 9096])).
% 2.64/2.82 tff(9757,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3668, 9756])).
% 2.64/2.82 tff(9758,plain,
% 2.64/2.82 (~r(z, s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5575, 9753, 95, 9723])).
% 2.64/2.82 tff(9759,plain,
% 2.64/2.82 (b(z, s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[293, 9758])).
% 2.64/2.82 tff(9760,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9761,plain,
% 2.64/2.82 (((~b(s(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(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9762,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[9761])).
% 2.64/2.82 tff(9763,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[9762, 9760])).
% 2.64/2.82 tff(9764,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(9765,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[9764, 9763])).
% 2.64/2.82 tff(9766,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9765, 171, 3281, 1275, 1384, 6462, 357, 2527])).
% 2.64/2.82 tff(9767,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9768,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9767, 1384, 1275, 9096, 9755, 9759])).
% 2.64/2.82 tff(9769,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6475, 9768])).
% 2.64/2.82 tff(9770,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9195, 9769, 9751, 9757])).
% 2.64/2.82 tff(9771,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2614, 9770])).
% 2.64/2.82 tff(9772,plain,
% 2.64/2.82 (~r(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9273, 9771, 9723, 259, 9753, 9741, 1275, 95])).
% 2.64/2.82 tff(9773,plain,
% 2.64/2.82 (~b(s(z), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8446, 9771, 1275, 1384])).
% 2.64/2.82 tff(9774,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1996, 9773, 9772])).
% 2.64/2.82 tff(9775,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9776,plain,
% 2.64/2.82 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9775, 259, 1275, 95])).
% 2.64/2.82 tff(9777,plain,
% 2.64/2.82 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1368, 9776])).
% 2.64/2.82 tff(9778,plain,
% 2.64/2.82 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7068, 9757, 9493, 9751])).
% 2.64/2.82 tff(9779,plain,
% 2.64/2.82 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[454, 9778, 254])).
% 2.64/2.82 tff(9780,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8834, 9777, 9493, 9757])).
% 2.64/2.82 tff(9781,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2842, 9780, 2264])).
% 2.64/2.82 tff(9782,plain,
% 2.64/2.82 (~b(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8545, 9781, 9755, 9779])).
% 2.64/2.82 tff(9783,plain,
% 2.64/2.82 (r(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1173, 9782])).
% 2.64/2.82 tff(9784,plain,
% 2.64/2.82 (~r(z, s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9166, 9753, 9723, 95])).
% 2.64/2.82 tff(9785,plain,
% 2.64/2.82 (b(z, s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9192, 9784])).
% 2.64/2.82 tff(9786,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8576, 9777, 9751, 9755, 9779, 9757])).
% 2.64/2.82 tff(9787,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2614, 9786])).
% 2.64/2.82 tff(9788,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9700, 9787, 9785, 9759, 9781])).
% 2.64/2.82 tff(9789,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[6475, 9788])).
% 2.64/2.82 tff(9790,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8843, 9789, 9783, 9493, 9777])).
% 2.64/2.82 tff(9791,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9792,plain,
% 2.64/2.82 (~b(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9791, 1275, 95])).
% 2.64/2.82 tff(9793,plain,
% 2.64/2.82 (r(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[244, 9792])).
% 2.64/2.82 tff(9794,plain,
% 2.64/2.82 (~r(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[5959, 9501, 9723, 95])).
% 2.64/2.82 tff(9795,plain,
% 2.64/2.82 (b(s(s(z)), z)),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[157, 9794])).
% 2.64/2.82 tff(9796,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8790, 9795, 9493, 1275, 9723, 9793, 4, 9501])).
% 2.64/2.82 tff(9797,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3668, 9796])).
% 2.64/2.82 tff(9798,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9676, 9797, 1275, 9096])).
% 2.64/2.82 tff(9799,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[321, 9798, 255])).
% 2.64/2.82 tff(9800,plain,
% 2.64/2.82 (~b(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9567, 9799, 95, 9793, 9493, 9491])).
% 2.64/2.82 tff(9801,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9802,plain,
% 2.64/2.82 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9803,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[9802])).
% 2.64/2.82 tff(9804,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[9803, 9801])).
% 2.64/2.82 tff(9805,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(9806,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[9805, 9804])).
% 2.64/2.82 tff(9807,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9806, 171, 3686, 1275, 4, 376])).
% 2.64/2.82 tff(9808,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9809,plain,
% 2.64/2.82 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9808, 9797, 1275, 4])).
% 2.64/2.82 tff(9810,plain,
% 2.64/2.82 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[454, 9809, 254])).
% 2.64/2.82 tff(9811,plain,
% 2.64/2.82 (~r(z, s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9654, 9810, 1275, 9096, 95, 9723, 9797, 9795])).
% 2.64/2.82 tff(9812,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[124, 9811, 9800])).
% 2.64/2.82 tff(9813,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9814,plain,
% 2.64/2.82 (~b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9813, 8041, 31])).
% 2.64/2.82 tff(9815,plain,
% 2.64/2.82 (r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[479, 9814])).
% 2.64/2.82 tff(9816,plain,
% 2.64/2.82 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9538, 9815, 9487, 31])).
% 2.64/2.82 tff(9817,plain,
% 2.64/2.82 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[321, 9816, 255])).
% 2.64/2.82 tff(9818,plain,
% 2.64/2.82 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9676, 9817, 8041, 9090])).
% 2.64/2.82 tff(9819,plain,
% 2.64/2.82 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[3668, 9818])).
% 2.64/2.82 tff(9820,plain,
% 2.64/2.82 (~b(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9791, 8041, 31])).
% 2.64/2.82 tff(9821,plain,
% 2.64/2.82 (r(s(s(z)), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[244, 9820])).
% 2.64/2.82 tff(9822,plain,
% 2.64/2.82 (~b(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9721, 31, 8041])).
% 2.64/2.82 tff(9823,plain,
% 2.64/2.82 (r(s(z), s(s(z)))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[550, 9822])).
% 2.64/2.82 tff(9824,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9352, 9815, 9823, 9821])).
% 2.64/2.82 tff(9825,plain,
% 2.64/2.82 (b(s(s(s(z))), s(z))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1173, 9824])).
% 2.64/2.82 tff(9826,plain,
% 2.64/2.82 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[7068, 9819, 9487, 9815])).
% 2.64/2.82 tff(9827,plain,
% 2.64/2.82 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[454, 9826, 254])).
% 2.64/2.82 tff(9828,plain,
% 2.64/2.82 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8545, 9827, 9817, 9825])).
% 2.64/2.82 tff(9829,plain,
% 2.64/2.82 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2842, 9828, 2264])).
% 2.64/2.82 tff(9830,plain,
% 2.64/2.82 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8834, 9829, 9487, 9819])).
% 2.64/2.82 tff(9831,plain,
% 2.64/2.82 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[1368, 9830])).
% 2.64/2.82 tff(9832,plain,
% 2.64/2.82 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8535, 9829, 9815, 9819])).
% 2.64/2.82 tff(9833,plain,
% 2.64/2.82 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[2614, 9832])).
% 2.64/2.82 tff(9834,plain,
% 2.64/2.82 ($false),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[8606, 171, 9825, 9833, 8041, 9831])).
% 2.64/2.82 tff(9835,plain,(b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.64/2.82 tff(9836,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9837,plain,
% 2.64/2.82 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9838,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.82 inference(monotonicity,[status(thm)],[9837])).
% 2.64/2.82 tff(9839,plain,
% 2.64/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.82 inference(transitivity,[status(thm)],[9838, 9836])).
% 2.64/2.82 tff(9840,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(quant_inst,[status(thm)],[])).
% 2.64/2.82 tff(9841,plain,
% 2.64/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.82 inference(modus_ponens,[status(thm)],[9840, 9839])).
% 2.64/2.82 tff(9842,plain,
% 2.64/2.82 (~b(z, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[9841, 171, 3281, 9835, 4])).
% 2.64/2.82 tff(9843,plain,
% 2.64/2.82 (r(z, s(s(s(s(s(z))))))),
% 2.64/2.82 inference(unit_resolution,[status(thm)],[498, 9842])).
% 2.64/2.82 tff(9844,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9845,plain,
% 2.64/2.82 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.82 inference(rewrite,[status(thm)],[])).
% 2.64/2.82 tff(9846,plain,
% 2.64/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9845])).
% 2.64/2.83 tff(9847,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9846, 9844])).
% 2.64/2.83 tff(9848,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9849,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9848, 9847])).
% 2.64/2.83 tff(9850,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9849, 106, 96, 126, 502])).
% 2.64/2.83 tff(9851,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[145, 9850])).
% 2.64/2.83 tff(9852,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9853,plain,
% 2.64/2.83 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9854,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9853])).
% 2.64/2.83 tff(9855,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9854, 9852])).
% 2.64/2.83 tff(9856,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9857,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9856, 9855])).
% 2.64/2.83 tff(9858,plain,
% 2.64/2.83 (~r(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9857, 106, 96, 126, 502])).
% 2.64/2.83 tff(9859,plain,
% 2.64/2.83 (b(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[498, 9858])).
% 2.64/2.83 tff(9860,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[5694, 2, 126, 502])).
% 2.64/2.83 tff(9861,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[225, 9860])).
% 2.64/2.83 tff(9862,plain,
% 2.64/2.83 (~b(s(s(z)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[6961, 9861, 9859, 9851])).
% 2.64/2.83 tff(9863,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9864,plain,
% 2.64/2.83 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9865,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9864])).
% 2.64/2.83 tff(9866,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9865, 9863])).
% 2.64/2.83 tff(9867,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9868,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9867, 9866])).
% 2.64/2.83 tff(9869,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9868, 171, 323, 5625, 5617, 3133])).
% 2.64/2.83 tff(9870,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(9871,plain,
% 2.64/2.83 ((~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9870, 9835])).
% 2.64/2.83 tff(9872,plain,
% 2.64/2.83 (~b(s(z), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9871, 2, 96, 126])).
% 2.64/2.83 tff(9873,plain,
% 2.64/2.83 (r(s(z), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[550, 9872])).
% 2.64/2.83 tff(9874,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9875,plain,
% 2.64/2.83 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9876,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9875])).
% 2.64/2.83 tff(9877,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9876, 9874])).
% 2.64/2.83 tff(9878,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9879,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9878, 9877])).
% 2.64/2.83 tff(9880,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9879, 106, 554, 96, 2, 637])).
% 2.64/2.83 tff(9881,plain,((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(9882,plain,
% 2.64/2.83 (~r(s(s(z)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9881, 9873, 96, 2])).
% 2.64/2.83 tff(9883,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[157, 9882, 9862])).
% 2.64/2.83 tff(9884,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(9885,plain,
% 2.64/2.83 (~r(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9884, 502, 126, 96])).
% 2.64/2.83 tff(9886,plain,
% 2.64/2.83 (b(s(s(z)), s(z))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[244, 9885])).
% 2.64/2.83 tff(9887,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9888,plain,
% 2.64/2.83 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9889,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9888])).
% 2.64/2.83 tff(9890,plain,
% 2.64/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9889, 9887])).
% 2.64/2.83 tff(9891,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9892,plain,
% 2.64/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9891, 9890])).
% 2.64/2.83 tff(9893,plain,
% 2.64/2.83 (~r(s(s(s(s(s(z))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9892, 106, 554, 96, 502])).
% 2.64/2.83 tff(9894,plain,
% 2.64/2.83 (b(s(s(s(s(s(z))))), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[143, 25, 140, 9893])).
% 2.64/2.83 tff(9895,plain,
% 2.64/2.83 (~r(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[562, 106, 554, 96, 502])).
% 2.64/2.83 tff(9896,plain,
% 2.64/2.83 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[496, 25, 9895])).
% 2.64/2.83 tff(9897,plain,
% 2.64/2.83 (b(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9896, 6021])).
% 2.64/2.83 tff(9898,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9899,plain,
% 2.64/2.83 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9900,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9899])).
% 2.64/2.83 tff(9901,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9900, 9898])).
% 2.64/2.83 tff(9902,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9903,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9902, 9901])).
% 2.64/2.83 tff(9904,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9903, 171, 259, 1, 3133, 9894, 9897])).
% 2.64/2.83 tff(9905,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(9906,plain,
% 2.64/2.83 (~b(s(s(z)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9905, 502, 96, 3133, 554, 259])).
% 2.64/2.83 tff(9907,plain,
% 2.64/2.83 (r(s(s(z)), z)),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[157, 9906])).
% 2.64/2.83 tff(9908,plain,
% 2.64/2.83 (~r(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[2549, 9907, 554, 96])).
% 2.64/2.83 tff(9909,plain,
% 2.64/2.83 (b(z, s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[124, 9908])).
% 2.64/2.83 tff(9910,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), 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(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), 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(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9911,plain,
% 2.64/2.83 (((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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(z))) | (~b(s(z), 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(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(rewrite,[status(thm)],[])).
% 2.64/2.83 tff(9912,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), 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(s(s(s(s(s(z))))), z))))),
% 2.64/2.83 inference(monotonicity,[status(thm)],[9911])).
% 2.64/2.83 tff(9913,plain,
% 2.64/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), 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(s(s(s(s(s(z))))), z)))),
% 2.64/2.83 inference(transitivity,[status(thm)],[9912, 9910])).
% 2.64/2.83 tff(9914,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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))))))))),
% 2.64/2.83 inference(quant_inst,[status(thm)],[])).
% 2.64/2.83 tff(9915,plain,
% 2.64/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.64/2.83 inference(modus_ponens,[status(thm)],[9914, 9913])).
% 2.64/2.83 tff(9916,plain,
% 2.64/2.83 (~b(z, s(s(s(s(s(z))))))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9915, 171, 259, 161, 3133, 207, 9894])).
% 2.64/2.83 tff(9917,plain,
% 2.64/2.83 ($false),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9896, 9916, 6021])).
% 2.64/2.83 tff(9918,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.83 tff(9919,plain,
% 2.64/2.83 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[9918, 9909, 96, 3133, 502, 554, 259])).
% 2.64/2.83 tff(9920,plain,
% 2.64/2.83 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.83 inference(unit_resolution,[status(thm)],[225, 9919])).
% 2.64/2.84 tff(9921,plain,
% 2.64/2.84 (~r(s(z), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3167, 9920, 9907, 554])).
% 2.64/2.84 tff(9922,plain,
% 2.64/2.84 (b(s(z), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[60, 9921])).
% 2.64/2.84 tff(9923,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9924,plain,
% 2.64/2.84 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9925,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9924])).
% 2.64/2.84 tff(9926,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9925, 9923])).
% 2.64/2.84 tff(9927,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9928,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[9927, 9926])).
% 2.64/2.84 tff(9929,plain,
% 2.64/2.84 (~b(z, s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9928, 171, 9909, 3133, 9922, 9894])).
% 2.64/2.84 tff(9930,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9896, 9929, 6021])).
% 2.64/2.84 tff(9931,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(9932,plain,
% 2.64/2.84 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9931, 9835])).
% 2.64/2.84 tff(9933,plain,
% 2.64/2.84 (~r(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9932, 9886, 96, 502])).
% 2.64/2.84 tff(9934,plain,
% 2.64/2.84 (b(s(z), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[550, 9933])).
% 2.64/2.84 tff(9935,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3668, 5751])).
% 2.64/2.84 tff(9936,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9937,plain,
% 2.64/2.84 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9938,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9937])).
% 2.64/2.84 tff(9939,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9938, 9936])).
% 2.64/2.84 tff(9940,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9941,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[9940, 9939])).
% 2.64/2.84 tff(9942,plain,
% 2.64/2.84 (~r(z, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9941, 106, 96, 126, 263])).
% 2.64/2.84 tff(9943,plain,
% 2.64/2.84 (b(z, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[293, 9942])).
% 2.64/2.84 tff(9944,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9945,plain,
% 2.64/2.84 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9946,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9945])).
% 2.64/2.84 tff(9947,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9946, 9944])).
% 2.64/2.84 tff(9948,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9949,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[9948, 9947])).
% 2.64/2.84 tff(9950,plain,
% 2.64/2.84 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9949, 106, 126, 502, 263])).
% 2.64/2.84 tff(9951,plain,
% 2.64/2.84 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[427, 9950])).
% 2.64/2.84 tff(9952,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[5548, 9951, 9943, 9859, 9935])).
% 2.64/2.84 tff(9953,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(9954,plain,
% 2.64/2.84 (~r(s(s(s(s(z)))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9953, 502, 126, 96])).
% 2.64/2.84 tff(9955,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(z)) | b(s(s(s(s(z)))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[321, 255])).
% 2.64/2.84 tff(9956,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), s(z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9955, 9954])).
% 2.64/2.84 tff(9957,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[365, 9956, 9886, 9934])).
% 2.64/2.84 tff(9958,plain,
% 2.64/2.84 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[374, 355])).
% 2.64/2.84 tff(9959,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9958, 9957])).
% 2.64/2.84 tff(9960,plain,
% 2.64/2.84 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6512, 9956, 9886, 9934])).
% 2.64/2.84 tff(9961,plain,
% 2.64/2.84 (r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[351, 9960])).
% 2.64/2.84 tff(9962,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9963,plain,
% 2.64/2.84 (((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9964,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9963])).
% 2.64/2.84 tff(9965,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9964, 9962])).
% 2.64/2.84 tff(9966,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9967,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[9966, 9965])).
% 2.64/2.84 tff(9968,plain,
% 2.64/2.84 (~b(z, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9967, 171, 3686, 159, 1313])).
% 2.64/2.84 tff(9969,plain,
% 2.64/2.84 (r(z, s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[293, 9968])).
% 2.64/2.84 tff(9970,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3692, 171, 3686, 159, 1313])).
% 2.64/2.84 tff(9971,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[274, 9970])).
% 2.64/2.84 tff(9972,plain,
% 2.64/2.84 (~r(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[6904, 9971, 96, 569])).
% 2.64/2.84 tff(9973,plain,
% 2.64/2.84 (b(s(s(z)), z)),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[157, 9972])).
% 2.64/2.84 tff(9974,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9975,plain,
% 2.64/2.84 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9976,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9975])).
% 2.64/2.84 tff(9977,plain,
% 2.64/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9976, 9974])).
% 2.64/2.84 tff(9978,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9979,plain,
% 2.64/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.64/2.84 inference(modus_ponens,[status(thm)],[9978, 9977])).
% 2.64/2.84 tff(9980,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9979, 171, 259, 161, 1, 3133])).
% 2.64/2.84 tff(9981,plain,((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(9982,plain,
% 2.64/2.84 ((~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9981, 9835])).
% 2.64/2.84 tff(9983,plain,
% 2.64/2.84 (~b(z, s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9982, 9973, 259])).
% 2.64/2.84 tff(9984,plain,
% 2.64/2.84 (r(z, s(s(z)))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[124, 9983])).
% 2.64/2.84 tff(9985,plain,
% 2.64/2.84 ($false),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[526, 106, 9984, 9969, 569, 500])).
% 2.64/2.84 tff(9986,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.84 tff(9987,plain,
% 2.64/2.84 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9986, 9959, 9961, 9886, 96, 9851, 9859])).
% 2.64/2.84 tff(9988,plain,
% 2.64/2.84 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[3668, 9987])).
% 2.64/2.84 tff(9989,plain,
% 2.64/2.84 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[534, 106, 9988, 126, 502])).
% 2.64/2.84 tff(9990,plain,
% 2.64/2.84 (r(s(z), s(s(s(s(z))))) | b(s(z), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[454, 254])).
% 2.64/2.84 tff(9991,plain,
% 2.64/2.84 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.84 inference(unit_resolution,[status(thm)],[9990, 9989])).
% 2.64/2.84 tff(9992,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9993,plain,
% 2.64/2.84 (((~r(s(s(z)), s(s(s(s(z)))))) | (~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)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.84 inference(rewrite,[status(thm)],[])).
% 2.64/2.84 tff(9994,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.64/2.84 inference(monotonicity,[status(thm)],[9993])).
% 2.64/2.84 tff(9995,plain,
% 2.64/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.84 inference(transitivity,[status(thm)],[9994, 9992])).
% 2.64/2.84 tff(9996,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.84 inference(quant_inst,[status(thm)],[])).
% 2.64/2.84 tff(9997,plain,
% 2.64/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[9996, 9995])).
% 2.64/2.85 tff(9998,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9997, 106, 600, 569, 500])).
% 2.64/2.85 tff(9999,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[274, 9998])).
% 2.64/2.85 tff(10000,plain,
% 2.64/2.85 (~r(z, s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[526, 106, 600, 569, 500])).
% 2.64/2.85 tff(10001,plain,
% 2.64/2.85 (b(z, s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[293, 10000])).
% 2.64/2.85 tff(10002,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10003,plain,
% 2.64/2.85 (((~b(s(s(s(s(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(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10004,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10003])).
% 2.64/2.85 tff(10005,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[10004, 10002])).
% 2.64/2.85 tff(10006,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(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)))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(10007,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[10006, 10005])).
% 2.64/2.85 tff(10008,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10007, 171, 9835, 376, 357, 10001, 9999])).
% 2.64/2.85 tff(10009,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(10010,plain,
% 2.64/2.85 (~r(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10009, 9991, 9956, 9959, 9961])).
% 2.64/2.85 tff(10011,plain,
% 2.64/2.85 (b(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[124, 10010])).
% 2.64/2.85 tff(10012,plain,
% 2.64/2.85 (~b(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9982, 10011, 9886])).
% 2.64/2.85 tff(10013,plain,
% 2.64/2.85 (r(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[157, 10012])).
% 2.64/2.85 tff(10014,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6904, 10013, 96, 9959])).
% 2.64/2.85 tff(10015,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[274, 10014])).
% 2.64/2.85 tff(10016,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10017,plain,
% 2.64/2.85 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), 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(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10018,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10017])).
% 2.64/2.85 tff(10019,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.64/2.85 inference(transitivity,[status(thm)],[10018, 10016])).
% 2.64/2.85 tff(10020,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), 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)))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(10021,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[10020, 10019])).
% 2.64/2.85 tff(10022,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10021, 171, 9886, 10011, 9835, 9991, 9956, 10015])).
% 2.64/2.85 tff(10023,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(10024,plain,
% 2.64/2.85 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10023, 96, 126])).
% 2.64/2.85 tff(10025,plain,
% 2.64/2.85 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[479, 10024])).
% 2.64/2.85 tff(10026,plain,
% 2.64/2.85 (b(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[157, 9882])).
% 2.64/2.85 tff(10027,plain,
% 2.64/2.85 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[4802, 9873, 126, 2])).
% 2.64/2.85 tff(10028,plain,
% 2.64/2.85 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[225, 10027])).
% 2.64/2.85 tff(10029,plain,
% 2.64/2.85 (~r(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[8816, 106, 9873, 96, 2])).
% 2.64/2.85 tff(10030,plain,
% 2.64/2.85 (b(z, s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[124, 10029])).
% 2.64/2.85 tff(10031,plain,
% 2.64/2.85 (~b(s(s(s(s(s(z))))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[215, 10030, 10028, 10026])).
% 2.64/2.85 tff(10032,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[145, 10031])).
% 2.64/2.85 tff(10033,plain,
% 2.64/2.85 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5678, 10032, 126, 10025])).
% 2.64/2.85 tff(10034,plain,
% 2.64/2.85 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[3668, 10033])).
% 2.64/2.85 tff(10035,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[634, 83, 161, 207, 1])).
% 2.64/2.85 tff(10036,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9958, 10035])).
% 2.64/2.85 tff(10037,plain,
% 2.64/2.85 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[6394, 83, 3686, 4])).
% 2.64/2.85 tff(10038,plain,
% 2.64/2.85 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9990, 10037])).
% 2.64/2.85 tff(10039,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5989, 106, 554, 2, 10038, 10036])).
% 2.64/2.85 tff(10040,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(10041,plain,
% 2.64/2.85 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10040, 9873, 2, 10030, 10028, 10026, 10034, 10025])).
% 2.64/2.85 tff(10042,plain,
% 2.64/2.85 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[427, 10041])).
% 2.64/2.85 tff(10043,plain,
% 2.64/2.85 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[7134, 10042, 126, 9873])).
% 2.64/2.85 tff(10044,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[205, 10043])).
% 2.64/2.85 tff(10045,plain,
% 2.64/2.85 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5760, 10044, 10028, 10034])).
% 2.64/2.85 tff(10046,plain,
% 2.64/2.85 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9958, 10045])).
% 2.64/2.85 tff(10047,plain,
% 2.64/2.85 (~r(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[5989, 106, 9873, 2, 10046])).
% 2.64/2.85 tff(10048,plain,
% 2.64/2.85 (b(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9990, 10047])).
% 2.64/2.85 tff(10049,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10050,plain,
% 2.64/2.85 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10051,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10050])).
% 2.64/2.85 tff(10052,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[10051, 10049])).
% 2.64/2.85 tff(10053,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(10054,plain,
% 2.64/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[10053, 10052])).
% 2.64/2.85 tff(10055,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10054, 171, 10034, 10025, 10048, 357])).
% 2.64/2.85 tff(10056,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(10057,plain,
% 2.64/2.85 (~r(s(s(z)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10056, 357, 126, 96])).
% 2.64/2.85 tff(10058,plain,
% 2.64/2.85 (b(s(s(z)), s(z))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[244, 10057])).
% 2.64/2.85 tff(10059,plain,
% 2.64/2.85 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[445, 10058, 10025, 357])).
% 2.64/2.85 tff(10060,plain,
% 2.64/2.85 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[9990, 10059])).
% 2.64/2.85 tff(10061,plain,
% 2.64/2.85 (~b(s(z), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[473, 260, 126, 10025, 357, 10058])).
% 2.64/2.85 tff(10062,plain,
% 2.64/2.85 (r(s(z), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[550, 10061])).
% 2.64/2.85 tff(10063,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10064,plain,
% 2.64/2.85 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~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(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10065,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10064])).
% 2.64/2.85 tff(10066,plain,
% 2.64/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.85 inference(transitivity,[status(thm)],[10065, 10063])).
% 2.64/2.85 tff(10067,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.64/2.85 inference(quant_inst,[status(thm)],[])).
% 2.64/2.85 tff(10068,plain,
% 2.64/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.64/2.85 inference(modus_ponens,[status(thm)],[10067, 10066])).
% 2.64/2.85 tff(10069,plain,
% 2.64/2.85 ($false),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10068, 106, 554, 260, 3, 500])).
% 2.64/2.85 tff(10070,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.85 tff(10071,plain,
% 2.64/2.85 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[10070, 10062, 260, 10060])).
% 2.64/2.85 tff(10072,plain,
% 2.64/2.85 (b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[351, 10071])).
% 2.64/2.85 tff(10073,plain,
% 2.64/2.85 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[463, 260, 126, 10060])).
% 2.64/2.85 tff(10074,plain,
% 2.64/2.85 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[225, 10073])).
% 2.64/2.85 tff(10075,plain,
% 2.64/2.85 (~r(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[2549, 10062, 96, 600])).
% 2.64/2.85 tff(10076,plain,
% 2.64/2.85 (b(s(s(z)), z)),
% 2.64/2.85 inference(unit_resolution,[status(thm)],[157, 10075])).
% 2.64/2.85 tff(10077,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10078,plain,
% 2.64/2.85 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.85 inference(rewrite,[status(thm)],[])).
% 2.64/2.85 tff(10079,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.64/2.85 inference(monotonicity,[status(thm)],[10078])).
% 2.64/2.85 tff(10080,plain,
% 2.64/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10079, 10077])).
% 2.64/2.86 tff(10081,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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)))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10082,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10081, 10080])).
% 2.64/2.86 tff(10083,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10082, 171, 1, 9835, 83, 207, 357, 2352])).
% 2.64/2.86 tff(10084,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10085,plain,
% 2.64/2.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10084, 10076, 10074, 357, 10072])).
% 2.64/2.86 tff(10086,plain,
% 2.64/2.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[427, 10085])).
% 2.64/2.86 tff(10087,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10088,plain,
% 2.64/2.86 (((~r(s(s(s(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(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10089,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[10088])).
% 2.64/2.86 tff(10090,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10089, 10087])).
% 2.64/2.86 tff(10091,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10092,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10091, 10090])).
% 2.64/2.86 tff(10093,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10092, 106, 260, 10086, 126, 10060])).
% 2.64/2.86 tff(10094,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10095,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10094, 600, 357, 96, 126])).
% 2.64/2.86 tff(10096,plain,
% 2.64/2.86 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3668, 10095])).
% 2.64/2.86 tff(10097,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[1151, 171, 323, 259, 3686, 4, 357])).
% 2.64/2.86 tff(10098,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10099,plain,
% 2.64/2.86 (~b(s(z), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10098, 10096, 10058, 10025, 357])).
% 2.64/2.86 tff(10100,plain,
% 2.64/2.86 (r(s(z), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[550, 10099])).
% 2.64/2.86 tff(10101,plain,
% 2.64/2.86 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[624, 10100, 96, 600])).
% 2.64/2.86 tff(10102,plain,
% 2.64/2.86 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[205, 10101])).
% 2.64/2.86 tff(10103,plain,
% 2.64/2.86 (~r(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[2549, 10100, 96, 600])).
% 2.64/2.86 tff(10104,plain,
% 2.64/2.86 (b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[157, 10103])).
% 2.64/2.86 tff(10105,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10106,plain,
% 2.64/2.86 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(z), z)) | (~b(s(s(z)), 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10107,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[10106])).
% 2.64/2.86 tff(10108,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10107, 10105])).
% 2.64/2.86 tff(10109,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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)))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10110,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10109, 10108])).
% 2.64/2.86 tff(10111,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10110, 171, 10104, 9835, 10096, 10025, 10102])).
% 2.64/2.86 tff(10112,plain,
% 2.64/2.86 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9958, 10111])).
% 2.64/2.86 tff(10113,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10114,plain,
% 2.64/2.86 (((~r(s(s(s(s(z)))), s(s(z)))) | (~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(z)))) | (~r(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)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10115,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[10114])).
% 2.64/2.86 tff(10116,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10115, 10113])).
% 2.64/2.86 tff(10117,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10118,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10117, 10116])).
% 2.64/2.86 tff(10119,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10118, 106, 554, 3, 569, 500])).
% 2.64/2.86 tff(10120,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10121,plain,
% 2.64/2.86 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10120, 10100, 10060, 10112])).
% 2.64/2.86 tff(10122,plain,
% 2.64/2.86 (b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[351, 10121])).
% 2.64/2.86 tff(10123,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10124,plain,
% 2.64/2.86 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(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(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10125,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[10124])).
% 2.64/2.86 tff(10126,plain,
% 2.64/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10125, 10123])).
% 2.64/2.86 tff(10127,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(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))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10128,plain,
% 2.64/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10127, 10126])).
% 2.64/2.86 tff(10129,plain,
% 2.64/2.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10128, 171, 10096, 10025, 10102, 10122])).
% 2.64/2.86 tff(10130,plain,
% 2.64/2.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[427, 10129])).
% 2.64/2.86 tff(10131,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10132,plain,
% 2.64/2.86 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(rewrite,[status(thm)],[])).
% 2.64/2.86 tff(10133,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.86 inference(monotonicity,[status(thm)],[10132])).
% 2.64/2.86 tff(10134,plain,
% 2.64/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(transitivity,[status(thm)],[10133, 10131])).
% 2.64/2.86 tff(10135,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.86 inference(quant_inst,[status(thm)],[])).
% 2.64/2.86 tff(10136,plain,
% 2.64/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.86 inference(modus_ponens,[status(thm)],[10135, 10134])).
% 2.64/2.86 tff(10137,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10136, 106, 10130, 126, 10060, 10112])).
% 2.64/2.86 tff(10138,plain,((~r(z, s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10139,plain,
% 2.64/2.86 (~r(z, s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10138, 357, 96, 126])).
% 2.64/2.86 tff(10140,plain,
% 2.64/2.86 (b(z, s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[124, 10139])).
% 2.64/2.86 tff(10141,plain,
% 2.64/2.86 (~b(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[9982, 10140, 10058])).
% 2.64/2.86 tff(10142,plain,
% 2.64/2.86 (r(s(s(z)), z)),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[157, 10141])).
% 2.64/2.86 tff(10143,plain,
% 2.64/2.86 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[473, 323, 126, 4, 357, 259])).
% 2.64/2.86 tff(10144,plain,
% 2.64/2.86 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10098, 323, 259, 4, 357])).
% 2.64/2.86 tff(10145,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3668, 10144, 10143])).
% 2.64/2.86 tff(10146,plain,((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10147,plain,
% 2.64/2.86 (~b(s(z), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[10146, 10058, 10025, 357, 126])).
% 2.64/2.86 tff(10148,plain,
% 2.64/2.86 (r(s(z), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[550, 10147])).
% 2.64/2.86 tff(10149,plain,
% 2.64/2.86 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[3167, 10148, 126, 10142])).
% 2.64/2.86 tff(10150,plain,
% 2.64/2.86 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[225, 10149])).
% 2.64/2.86 tff(10151,plain,
% 2.64/2.86 ($false),
% 2.64/2.86 inference(unit_resolution,[status(thm)],[8352, 106, 96, 260, 5567, 3])).
% 2.64/2.86 tff(10152,plain,((~r(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.86 tff(10153,plain,
% 2.64/2.86 (~r(z, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10152, 260, 96, 10060])).
% 2.64/2.87 tff(10154,plain,
% 2.64/2.87 (b(z, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[293, 10153])).
% 2.64/2.87 tff(10155,plain,
% 2.64/2.87 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10070, 260, 10148, 10060])).
% 2.64/2.87 tff(10156,plain,
% 2.64/2.87 (b(s(s(z)), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[351, 10155])).
% 2.64/2.87 tff(10157,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[5981, 10154, 10140, 10156])).
% 2.64/2.87 tff(10158,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9958, 10157])).
% 2.64/2.87 tff(10159,plain,
% 2.64/2.87 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[587, 10158, 10058, 10148, 260, 357])).
% 2.64/2.87 tff(10160,plain,
% 2.64/2.87 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[205, 10159])).
% 2.64/2.87 tff(10161,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10092, 106, 260, 5609, 126, 3])).
% 2.64/2.87 tff(10162,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(10163,plain,
% 2.64/2.87 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10162, 260, 126, 10060])).
% 2.64/2.87 tff(10164,plain,
% 2.64/2.87 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[427, 10163])).
% 2.64/2.87 tff(10165,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10166,plain,
% 2.64/2.87 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10167,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10166])).
% 2.64/2.87 tff(10168,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10167, 10165])).
% 2.64/2.87 tff(10169,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(10170,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[10169, 10168])).
% 2.64/2.87 tff(10171,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10170, 171, 10058, 9835, 10164, 10025, 10160, 10154])).
% 2.64/2.87 tff(10172,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(10173,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10172, 357, 96, 126])).
% 2.64/2.87 tff(10174,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[3668, 10173])).
% 2.64/2.87 tff(10175,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10176,plain,
% 2.64/2.87 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(z))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10177,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10176])).
% 2.64/2.87 tff(10178,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), 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(z))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10177, 10175])).
% 2.64/2.87 tff(10179,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(10180,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[10179, 10178])).
% 2.64/2.87 tff(10181,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10180, 171, 10140, 9835, 10174, 10025, 10150, 357])).
% 2.64/2.87 tff(10182,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(10183,plain,
% 2.64/2.87 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10182, 96, 126])).
% 2.64/2.87 tff(10184,plain,
% 2.64/2.87 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9955, 10183])).
% 2.64/2.87 tff(10185,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10186,plain,
% 2.64/2.87 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10187,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10186])).
% 2.64/2.87 tff(10188,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10187, 10185])).
% 2.64/2.87 tff(10189,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(10190,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[10189, 10188])).
% 2.64/2.87 tff(10191,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10190, 106, 96, 126, 263, 2118])).
% 2.64/2.87 tff(10192,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(10193,plain,
% 2.64/2.87 (~r(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10192, 10184, 126, 96])).
% 2.64/2.87 tff(10194,plain,
% 2.64/2.87 (b(s(s(s(s(z)))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[274, 10193])).
% 2.64/2.87 tff(10195,plain,
% 2.64/2.87 (~r(z, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9941, 106, 96, 126, 10184])).
% 2.64/2.87 tff(10196,plain,
% 2.64/2.87 (b(z, s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[293, 10195])).
% 2.64/2.87 tff(10197,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10198,plain,
% 2.64/2.87 (((~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)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10199,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10198])).
% 2.64/2.87 tff(10200,plain,
% 2.64/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10199, 10197])).
% 2.64/2.87 tff(10201,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(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)))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(10202,plain,
% 2.64/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[10201, 10200])).
% 2.64/2.87 tff(10203,plain,
% 2.64/2.87 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10202, 171, 9835, 10196, 10194])).
% 2.64/2.87 tff(10204,plain,
% 2.64/2.87 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[9990, 10203])).
% 2.64/2.87 tff(10205,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10206,plain,
% 2.64/2.87 (((~r(s(s(s(s(z)))), s(z))) | (~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(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10207,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10206])).
% 2.64/2.87 tff(10208,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10207, 10205])).
% 2.64/2.87 tff(10209,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.87 tff(10210,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.87 inference(modus_ponens,[status(thm)],[10209, 10208])).
% 2.64/2.87 tff(10211,plain,
% 2.64/2.87 ($false),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10210, 106, 5609, 126, 3, 263])).
% 2.64/2.87 tff(10212,plain,((~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)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.87 tff(10213,plain,
% 2.64/2.87 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[10212, 10204, 126, 10184])).
% 2.64/2.87 tff(10214,plain,
% 2.64/2.87 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[427, 10213])).
% 2.64/2.87 tff(10215,plain,
% 2.64/2.87 (~b(z, s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[8065, 171, 10214, 10196, 10194])).
% 2.64/2.87 tff(10216,plain,
% 2.64/2.87 (r(z, s(s(s(s(s(z))))))),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[498, 10215])).
% 2.64/2.87 tff(10217,plain,
% 2.64/2.87 (~b(s(s(s(s(s(z))))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[310, 171, 10214, 10196, 10194])).
% 2.64/2.87 tff(10218,plain,
% 2.64/2.87 (r(s(s(s(s(s(z))))), z)),
% 2.64/2.87 inference(unit_resolution,[status(thm)],[145, 10217])).
% 2.64/2.87 tff(10219,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10220,plain,
% 2.64/2.87 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(rewrite,[status(thm)],[])).
% 2.64/2.87 tff(10221,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.87 inference(monotonicity,[status(thm)],[10220])).
% 2.64/2.87 tff(10222,plain,
% 2.64/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.87 inference(transitivity,[status(thm)],[10221, 10219])).
% 2.64/2.87 tff(10223,plain,
% 2.64/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(z))))),
% 2.64/2.87 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10224,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10223, 10222])).
% 2.64/2.88 tff(10225,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10224, 106, 96, 126, 10218, 10216])).
% 2.64/2.88 tff(10226,plain,((~r(z, s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(10227,plain,
% 2.64/2.88 (~r(z, s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10226, 126])).
% 2.64/2.88 tff(10228,plain,
% 2.64/2.88 (b(z, s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[93, 10227])).
% 2.64/2.88 tff(10229,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10230,plain,
% 2.64/2.88 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10231,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10230])).
% 2.64/2.88 tff(10232,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10231, 10229])).
% 2.64/2.88 tff(10233,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10234,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10233, 10232])).
% 2.64/2.88 tff(10235,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10234, 171, 323, 3281, 1, 3133])).
% 2.64/2.88 tff(10236,plain,((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(10237,plain,
% 2.64/2.88 ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10236, 9835])).
% 2.64/2.88 tff(10238,plain,
% 2.64/2.88 (~b(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10237, 323, 10228])).
% 2.64/2.88 tff(10239,plain,
% 2.64/2.88 (r(s(s(z)), z)),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[157, 10238])).
% 2.64/2.88 tff(10240,plain,
% 2.64/2.88 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[205, 5734])).
% 2.64/2.88 tff(10241,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10242,plain,
% 2.64/2.88 (((~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(z))))), 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(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10243,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10242])).
% 2.64/2.88 tff(10244,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10243, 10241])).
% 2.64/2.88 tff(10245,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z))))), 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(s(z))), s(s(z)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10246,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10245, 10244])).
% 2.64/2.88 tff(10247,plain,
% 2.64/2.88 (~b(s(s(s(z))), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10246, 171, 838, 160, 207])).
% 2.64/2.88 tff(10248,plain,
% 2.64/2.88 (r(s(s(s(z))), s(s(z)))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2642, 10247])).
% 2.64/2.88 tff(10249,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10250,plain,
% 2.64/2.88 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10251,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10250])).
% 2.64/2.88 tff(10252,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10251, 10249])).
% 2.64/2.88 tff(10253,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10254,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10253, 10252])).
% 2.64/2.88 tff(10255,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10254, 106, 2, 126, 1199, 747])).
% 2.64/2.88 tff(10256,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(10257,plain,
% 2.64/2.88 (~r(s(s(s(z))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10256, 10248, 126, 2])).
% 2.64/2.88 tff(10258,plain,
% 2.64/2.88 (b(s(s(s(z))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1173, 10257])).
% 2.64/2.88 tff(10259,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10260,plain,
% 2.64/2.88 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10261,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10260])).
% 2.64/2.88 tff(10262,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10261, 10259])).
% 2.64/2.88 tff(10263,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10264,plain,
% 2.64/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10263, 10262])).
% 2.64/2.88 tff(10265,plain,
% 2.64/2.88 ((~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10264, 171, 323, 10228, 838, 160])).
% 2.64/2.88 tff(10266,plain,
% 2.64/2.88 (~b(z, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10265, 10258])).
% 2.64/2.88 tff(10267,plain,
% 2.64/2.88 (r(z, s(s(s(z))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[9192, 10266])).
% 2.64/2.88 tff(10268,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10269,plain,
% 2.64/2.88 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10270,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10269])).
% 2.64/2.88 tff(10271,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10270, 10268])).
% 2.64/2.88 tff(10272,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10273,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10272, 10271])).
% 2.64/2.88 tff(10274,plain,
% 2.64/2.88 ($false),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10273, 106, 2, 600, 10248, 10267])).
% 2.64/2.88 tff(10275,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.88 tff(10276,plain,
% 2.64/2.88 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10275, 600, 2, 323, 10240, 126, 9861])).
% 2.64/2.88 tff(10277,plain,
% 2.64/2.88 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[2614, 10276])).
% 2.64/2.88 tff(10278,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10279,plain,
% 2.64/2.88 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10280,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10279])).
% 2.64/2.88 tff(10281,plain,
% 2.64/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.88 inference(transitivity,[status(thm)],[10280, 10278])).
% 2.64/2.88 tff(10282,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.64/2.88 inference(quant_inst,[status(thm)],[])).
% 2.64/2.88 tff(10283,plain,
% 2.64/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.88 inference(modus_ponens,[status(thm)],[10282, 10281])).
% 2.64/2.88 tff(10284,plain,
% 2.64/2.88 (~r(s(s(s(z))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[10283, 106, 10277, 126, 502])).
% 2.64/2.88 tff(10285,plain,
% 2.64/2.88 (b(s(s(s(z))), s(z))),
% 2.64/2.88 inference(unit_resolution,[status(thm)],[1173, 10284])).
% 2.64/2.88 tff(10286,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10287,plain,
% 2.64/2.88 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.64/2.88 inference(rewrite,[status(thm)],[])).
% 2.64/2.88 tff(10288,plain,
% 2.64/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.64/2.88 inference(monotonicity,[status(thm)],[10287])).
% 2.64/2.88 tff(10289,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10288, 10286])).
% 2.64/2.89 tff(10290,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10291,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[10290, 10289])).
% 2.64/2.89 tff(10292,plain,
% 2.64/2.89 (~b(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10291, 171, 10228, 9835, 10285])).
% 2.64/2.89 tff(10293,plain,
% 2.64/2.89 (r(s(s(s(z))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[953, 25, 194, 10292])).
% 2.64/2.89 tff(10294,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8282, 106, 10239, 600, 10293])).
% 2.64/2.89 tff(10295,plain,
% 2.64/2.89 (b(s(s(s(z))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2642, 10294])).
% 2.64/2.89 tff(10296,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10297,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10298,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[10297])).
% 2.64/2.89 tff(10299,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10298, 10296])).
% 2.64/2.89 tff(10300,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10301,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[10300, 10299])).
% 2.64/2.89 tff(10302,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10301, 171, 323, 10285, 10295, 10240, 9861])).
% 2.64/2.89 tff(10303,plain,((~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(10304,plain,
% 2.64/2.89 (~r(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10303, 2, 126, 502, 323])).
% 2.64/2.89 tff(10305,plain,
% 2.64/2.89 (b(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[124, 10304])).
% 2.64/2.89 tff(10306,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10307,plain,
% 2.64/2.89 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10308,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[10307])).
% 2.64/2.89 tff(10309,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10308, 10306])).
% 2.64/2.89 tff(10310,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10311,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[10310, 10309])).
% 2.64/2.89 tff(10312,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10311, 171, 323, 10228, 10305, 10240, 9861])).
% 2.64/2.89 tff(10313,plain,((~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(10314,plain,
% 2.64/2.89 (~r(s(s(z)), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10313, 502, 126, 323])).
% 2.64/2.89 tff(10315,plain,
% 2.64/2.89 (b(s(s(z)), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[244, 10314])).
% 2.64/2.89 tff(10316,plain,
% 2.64/2.89 (~b(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[7045, 10315, 10228, 323])).
% 2.64/2.89 tff(10317,plain,
% 2.64/2.89 (r(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[124, 10316])).
% 2.64/2.89 tff(10318,plain,
% 2.64/2.89 (~b(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[7045, 259, 3281, 323])).
% 2.64/2.89 tff(10319,plain,
% 2.64/2.89 (r(z, s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[124, 10318])).
% 2.64/2.89 tff(10320,plain,
% 2.64/2.89 (~b(s(s(z)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10237, 323, 3281])).
% 2.64/2.89 tff(10321,plain,
% 2.64/2.89 (r(s(s(z)), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[157, 10320])).
% 2.64/2.89 tff(10322,plain,
% 2.64/2.89 ((~b(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))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9636, 9835])).
% 2.64/2.89 tff(10323,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10322, 357, 3281, 259])).
% 2.64/2.89 tff(10324,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9958, 10323])).
% 2.64/2.89 tff(10325,plain,
% 2.64/2.89 (~b(z, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[7254, 357, 3281, 323, 259])).
% 2.64/2.89 tff(10326,plain,
% 2.64/2.89 (r(z, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[293, 10325])).
% 2.64/2.89 tff(10327,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6247, 10326, 10324, 10321, 10319])).
% 2.64/2.89 tff(10328,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(10329,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10328, 10315, 323, 10228])).
% 2.64/2.89 tff(10330,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9955, 10329])).
% 2.64/2.89 tff(10331,plain,
% 2.64/2.89 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z)))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10332,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[10331])).
% 2.64/2.89 tff(10333,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10332, 5745])).
% 2.64/2.89 tff(10334,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(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(z))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10335,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[10334, 10333])).
% 2.64/2.89 tff(10336,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10335, 106, 260, 126, 502, 263])).
% 2.64/2.89 tff(10337,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(10338,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10337, 10330, 502, 126])).
% 2.64/2.89 tff(10339,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[3668, 10338])).
% 2.64/2.89 tff(10340,plain,
% 2.64/2.89 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6253, 376, 259, 323])).
% 2.64/2.89 tff(10341,plain,
% 2.64/2.89 (r(s(s(s(s(z)))), s(s(z)))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9958, 10340])).
% 2.64/2.89 tff(10342,plain,
% 2.64/2.89 (~r(s(s(s(s(z)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[3707, 10341, 637, 600])).
% 2.64/2.89 tff(10343,plain,
% 2.64/2.89 (b(s(s(s(s(z)))), z)),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[274, 10342])).
% 2.64/2.89 tff(10344,plain,
% 2.64/2.89 (~r(z, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[6247, 10341, 637, 600])).
% 2.64/2.89 tff(10345,plain,
% 2.64/2.89 (b(z, s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[293, 10344])).
% 2.64/2.89 tff(10346,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(z, s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10347,plain,
% 2.64/2.89 (((~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(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))))))) <=> ((~b(s(z), z)) | (~b(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(z, s(s(s(s(z)))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10348,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(z, s(s(s(s(z))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[10347])).
% 2.64/2.89 tff(10349,plain,
% 2.64/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(z, s(s(s(s(z)))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10348, 10346])).
% 2.64/2.89 tff(10350,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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)))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10351,plain,
% 2.64/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.64/2.89 inference(modus_ponens,[status(thm)],[10350, 10349])).
% 2.64/2.89 tff(10352,plain,
% 2.64/2.89 ($false),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10351, 171, 9835, 3686, 376, 10345, 10343])).
% 2.64/2.89 tff(10353,plain,((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.89 tff(10354,plain,
% 2.64/2.89 (~b(s(z), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10353, 10339, 10239, 10317, 10315, 323])).
% 2.64/2.89 tff(10355,plain,
% 2.64/2.89 (r(s(z), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[9990, 10354])).
% 2.64/2.89 tff(10356,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8249, 10355, 502, 10339])).
% 2.64/2.89 tff(10357,plain,
% 2.64/2.89 (b(s(s(s(z))), s(z))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1173, 10356])).
% 2.64/2.89 tff(10358,plain,
% 2.64/2.89 (~b(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8284, 10357, 10228, 10315])).
% 2.64/2.89 tff(10359,plain,
% 2.64/2.89 (r(s(z), s(s(s(z))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[1996, 10358])).
% 2.64/2.89 tff(10360,plain,
% 2.64/2.89 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[8177, 10359, 10330, 10355])).
% 2.64/2.89 tff(10361,plain,
% 2.64/2.89 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[2842, 2264])).
% 2.64/2.89 tff(10362,plain,
% 2.64/2.89 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.64/2.89 inference(unit_resolution,[status(thm)],[10361, 10360])).
% 2.64/2.89 tff(10363,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10364,plain,
% 2.64/2.89 (((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(rewrite,[status(thm)],[])).
% 2.64/2.89 tff(10365,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.64/2.89 inference(monotonicity,[status(thm)],[10364])).
% 2.64/2.89 tff(10366,plain,
% 2.64/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.64/2.89 inference(transitivity,[status(thm)],[10365, 10363])).
% 2.64/2.89 tff(10367,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))))),
% 2.64/2.89 inference(quant_inst,[status(thm)],[])).
% 2.64/2.89 tff(10368,plain,
% 2.64/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.64/2.90 inference(modus_ponens,[status(thm)],[10367, 10366])).
% 2.64/2.90 tff(10369,plain,
% 2.64/2.90 ($false),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[10368, 106, 2604, 126, 502, 1998])).
% 2.64/2.90 tff(10370,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.90 tff(10371,plain,
% 2.64/2.90 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[10370, 10359, 502, 126])).
% 2.64/2.90 tff(10372,plain,
% 2.64/2.90 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[2614, 10371])).
% 2.64/2.90 tff(10373,plain,
% 2.64/2.90 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[10212, 10355, 126, 10330])).
% 2.64/2.90 tff(10374,plain,
% 2.64/2.90 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[427, 10373])).
% 2.64/2.90 tff(10375,plain,
% 2.64/2.90 ($false),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[4223, 171, 10339, 10374, 10372, 10362])).
% 2.64/2.90 tff(10376,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.64/2.90 tff(10377,plain,
% 2.64/2.90 (~r(s(s(s(s(s(z))))), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[10376, 323, 126])).
% 2.64/2.90 tff(10378,plain,
% 2.64/2.90 (b(s(s(s(s(s(z))))), s(z))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[479, 10377])).
% 2.64/2.90 tff(10379,plain,
% 2.64/2.90 (~b(z, s(s(s(s(s(z))))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[9841, 171, 3281, 3133, 4])).
% 2.64/2.90 tff(10380,plain,
% 2.64/2.90 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[496, 25, 10379])).
% 2.64/2.90 tff(10381,plain,
% 2.64/2.90 (r(z, s(s(s(s(s(z))))))),
% 2.64/2.90 inference(unit_resolution,[status(thm)],[10380, 6021])).
% 2.64/2.90 tff(10382,plain,
% 2.64/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(10383,plain,
% 2.64/2.90 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.90 inference(rewrite,[status(thm)],[])).
% 2.64/2.90 tff(10384,plain,
% 2.64/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.64/2.90 inference(monotonicity,[status(thm)],[10383])).
% 2.64/2.90 tff(10385,plain,
% 2.64/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.90 inference(transitivity,[status(thm)],[10384, 10382])).
% 2.64/2.90 tff(10386,plain,
% 2.64/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.64/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(10387,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[10386, 10385])).
% 2.74/2.90 tff(10388,plain,
% 2.74/2.90 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10387, 171, 3281, 3133, 4])).
% 2.74/2.90 tff(10389,plain,
% 2.74/2.90 (r(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[143, 25, 140, 10388])).
% 2.74/2.90 tff(10390,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10391,plain,
% 2.74/2.90 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10392,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[10391])).
% 2.74/2.90 tff(10393,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[10392, 10390])).
% 2.74/2.90 tff(10394,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(10395,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[10394, 10393])).
% 2.74/2.90 tff(10396,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10395, 106, 637, 396, 10389, 10381])).
% 2.74/2.90 tff(10397,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(10398,plain,
% 2.74/2.90 ((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10397, 9835])).
% 2.74/2.90 tff(10399,plain,
% 2.74/2.90 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10398, 10378, 10228, 10239])).
% 2.74/2.90 tff(10400,plain,
% 2.74/2.90 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[225, 10399])).
% 2.74/2.90 tff(10401,plain,
% 2.74/2.90 (~b(z, s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[9841, 171, 10228, 9835, 10378])).
% 2.74/2.90 tff(10402,plain,
% 2.74/2.90 (r(z, s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[498, 10401])).
% 2.74/2.90 tff(10403,plain,
% 2.74/2.90 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10387, 171, 10228, 9835, 10378])).
% 2.74/2.90 tff(10404,plain,
% 2.74/2.90 (r(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[145, 10403])).
% 2.74/2.90 tff(10405,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10406,plain,
% 2.74/2.90 (((~r(z, s(s(s(s(s(z))))))) | (~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(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10407,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[10406])).
% 2.74/2.90 tff(10408,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[10407, 10405])).
% 2.74/2.90 tff(10409,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(10410,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[10409, 10408])).
% 2.74/2.90 tff(10411,plain,
% 2.74/2.90 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10410, 106, 10239, 10404, 10402])).
% 2.74/2.90 tff(10412,plain,
% 2.74/2.90 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[205, 10411])).
% 2.74/2.90 tff(10413,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10414,plain,
% 2.74/2.90 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(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))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10415,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[10414])).
% 2.74/2.90 tff(10416,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[10415, 10413])).
% 2.74/2.90 tff(10417,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(10418,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[10417, 10416])).
% 2.74/2.90 tff(10419,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10418, 171, 323, 10378, 10412, 10400])).
% 2.74/2.90 tff(10420,plain,((~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(10421,plain,
% 2.74/2.90 (~b(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10420, 126])).
% 2.74/2.90 tff(10422,plain,
% 2.74/2.90 (r(s(z), s(s(z)))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[550, 10421])).
% 2.74/2.90 tff(10423,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10291, 171, 3281, 9835, 1188, 1091])).
% 2.74/2.90 tff(10424,plain,((~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(10425,plain,
% 2.74/2.90 (~b(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10424, 1188, 3281])).
% 2.74/2.90 tff(10426,assumption,(~r(s(s(s(z))), z)), introduced(assumption)).
% 2.74/2.90 tff(10427,assumption,(~b(s(s(s(z))), z)), introduced(assumption)).
% 2.74/2.90 tff(10428,plain,
% 2.74/2.90 ($false),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[953, 25, 194, 10427, 10426])).
% 2.74/2.90 tff(10429,plain,(r(s(s(s(z))), z) | b(s(s(s(z))), z)), inference(lemma,lemma(discharge,[]))).
% 2.74/2.90 tff(10430,plain,
% 2.74/2.90 (r(s(s(s(z))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10429, 10425])).
% 2.74/2.90 tff(10431,plain,
% 2.74/2.90 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10387, 171, 3281, 9835, 4])).
% 2.74/2.90 tff(10432,plain,
% 2.74/2.90 (r(s(s(s(s(s(z))))), z)),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[145, 10431])).
% 2.74/2.90 tff(10433,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10434,plain,
% 2.74/2.90 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10435,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[10434])).
% 2.74/2.90 tff(10436,plain,
% 2.74/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.90 inference(transitivity,[status(thm)],[10435, 10433])).
% 2.74/2.90 tff(10437,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.90 inference(quant_inst,[status(thm)],[])).
% 2.74/2.90 tff(10438,plain,
% 2.74/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.90 inference(modus_ponens,[status(thm)],[10437, 10436])).
% 2.74/2.90 tff(10439,plain,
% 2.74/2.90 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[10438, 171, 3281, 9835, 1188, 4])).
% 2.74/2.90 tff(10440,plain,
% 2.74/2.90 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.90 inference(unit_resolution,[status(thm)],[2614, 10439])).
% 2.74/2.90 tff(10441,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~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)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10442,plain,
% 2.74/2.90 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~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)))),
% 2.74/2.90 inference(rewrite,[status(thm)],[])).
% 2.74/2.90 tff(10443,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~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))))),
% 2.74/2.90 inference(monotonicity,[status(thm)],[10442])).
% 2.74/2.90 tff(10444,plain,
% 2.74/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~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)))),
% 2.74/2.90 inference(transitivity,[status(thm)],[10443, 10441])).
% 2.74/2.90 tff(10445,plain,
% 2.74/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10446,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10445, 10444])).
% 2.74/2.91 tff(10447,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10446, 106, 10440, 10432, 9843, 10430])).
% 2.74/2.91 tff(10448,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10449,plain,
% 2.74/2.91 (~b(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10448, 4, 10228])).
% 2.74/2.91 tff(10450,plain,
% 2.74/2.91 (r(s(s(s(z))), s(z))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1173, 10449])).
% 2.74/2.91 tff(10451,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10452,plain,
% 2.74/2.91 (((~r(s(z), s(s(s(s(s(z))))))) | (~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(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10453,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))))) | (~r(s(s(s(z))), s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[10452])).
% 2.74/2.91 tff(10454,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[10453, 10451])).
% 2.74/2.91 tff(10455,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10456,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10455, 10454])).
% 2.74/2.91 tff(10457,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10456, 106, 2, 126, 747, 2678])).
% 2.74/2.91 tff(10458,plain,((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10459,plain,
% 2.74/2.91 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10458, 2, 126, 10450])).
% 2.74/2.91 tff(10460,assumption,(~b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 2.74/2.91 tff(10461,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[979, 25, 10460, 2569, 82])).
% 2.74/2.91 tff(10462,plain,(b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10463,plain,
% 2.74/2.91 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10462, 10459])).
% 2.74/2.91 tff(10464,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[4802, 2, 126, 10422])).
% 2.74/2.91 tff(10465,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[225, 10464])).
% 2.74/2.91 tff(10466,plain,
% 2.74/2.91 (~b(z, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9841, 171, 10228, 9835, 4])).
% 2.74/2.91 tff(10467,plain,
% 2.74/2.91 (r(z, s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[498, 10466])).
% 2.74/2.91 tff(10468,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10387, 171, 10228, 9835, 4])).
% 2.74/2.91 tff(10469,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), z)),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[145, 10468])).
% 2.74/2.91 tff(10470,plain,
% 2.74/2.91 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[5678, 10469, 126, 4])).
% 2.74/2.91 tff(10471,plain,
% 2.74/2.91 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3668, 10470])).
% 2.74/2.91 tff(10472,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10256, 2, 126, 10450])).
% 2.74/2.91 tff(10473,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2642, 10472])).
% 2.74/2.91 tff(10474,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10475,plain,
% 2.74/2.91 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), 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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10476,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[10475])).
% 2.74/2.91 tff(10477,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[10476, 10474])).
% 2.74/2.91 tff(10478,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10479,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10478, 10477])).
% 2.74/2.91 tff(10480,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10479, 171, 3686, 2705, 1384, 6462, 2740])).
% 2.74/2.91 tff(10481,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10482,plain,
% 2.74/2.91 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10481, 1384, 10471, 10473, 10463])).
% 2.74/2.91 tff(10483,plain,
% 2.74/2.91 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6475, 10482])).
% 2.74/2.91 tff(10484,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[3236, 106, 2604, 126, 127, 747])).
% 2.74/2.91 tff(10485,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10486,plain,
% 2.74/2.91 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10485, 10469, 126, 10450])).
% 2.74/2.91 tff(10487,plain,
% 2.74/2.91 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[2614, 10486])).
% 2.74/2.91 tff(10488,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10489,plain,
% 2.74/2.91 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10490,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[10489])).
% 2.74/2.91 tff(10491,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[10490, 10488])).
% 2.74/2.91 tff(10492,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10493,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10492, 10491])).
% 2.74/2.91 tff(10494,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10493, 171, 1976, 838, 1384, 4])).
% 2.74/2.91 tff(10495,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10496,plain,
% 2.74/2.91 (~b(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10495, 1384, 4, 10487])).
% 2.74/2.91 tff(10497,plain,
% 2.74/2.91 (r(s(z), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1996, 10496])).
% 2.74/2.91 tff(10498,plain,
% 2.74/2.91 (~r(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9141, 10497, 10450, 10483])).
% 2.74/2.91 tff(10499,plain,
% 2.74/2.91 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[9990, 10498])).
% 2.74/2.91 tff(10500,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10501,plain,
% 2.74/2.91 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(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(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10502,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[10501])).
% 2.74/2.91 tff(10503,plain,
% 2.74/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(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(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[10502, 10500])).
% 2.74/2.91 tff(10504,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(s(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(z)), s(s(s(s(s(z))))))))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10505,plain,
% 2.74/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10504, 10503])).
% 2.74/2.91 tff(10506,plain,
% 2.74/2.91 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10505, 171, 10487, 4, 10463])).
% 2.74/2.91 tff(10507,plain,
% 2.74/2.91 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10506, 1384])).
% 2.74/2.91 tff(10508,plain,
% 2.74/2.91 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[205, 10507])).
% 2.74/2.91 tff(10509,plain,
% 2.74/2.91 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6984, 10508, 126, 2])).
% 2.74/2.91 tff(10510,plain,
% 2.74/2.91 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[427, 10509])).
% 2.74/2.91 tff(10511,plain,
% 2.74/2.91 ($false),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[6394, 10510, 10499, 4, 10471])).
% 2.74/2.91 tff(10512,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.91 tff(10513,plain,
% 2.74/2.91 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[10512, 2, 126, 4])).
% 2.74/2.91 tff(10514,plain,
% 2.74/2.91 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.91 inference(unit_resolution,[status(thm)],[1368, 10513])).
% 2.74/2.91 tff(10515,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10516,plain,
% 2.74/2.91 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.74/2.91 inference(rewrite,[status(thm)],[])).
% 2.74/2.91 tff(10517,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 2.74/2.91 inference(monotonicity,[status(thm)],[10516])).
% 2.74/2.91 tff(10518,plain,
% 2.74/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 2.74/2.91 inference(transitivity,[status(thm)],[10517, 10515])).
% 2.74/2.91 tff(10519,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.74/2.91 inference(quant_inst,[status(thm)],[])).
% 2.74/2.91 tff(10520,plain,
% 2.74/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 2.74/2.91 inference(modus_ponens,[status(thm)],[10519, 10518])).
% 2.74/2.92 tff(10521,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10520, 106, 1357, 127, 747, 1975])).
% 2.74/2.92 tff(10522,plain,((~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10523,plain,
% 2.74/2.92 (~r(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10522, 10514, 10469, 10450])).
% 2.74/2.92 tff(10524,plain,
% 2.74/2.92 (b(z, s(s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9192, 10523])).
% 2.74/2.92 tff(10525,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10526,plain,
% 2.74/2.92 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10527,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[10526])).
% 2.74/2.92 tff(10528,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[10527, 10525])).
% 2.74/2.92 tff(10529,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(10530,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[10529, 10528])).
% 2.74/2.92 tff(10531,plain,
% 2.74/2.92 ((~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10530, 171, 10228, 10487, 4, 10463])).
% 2.74/2.92 tff(10532,plain,
% 2.74/2.92 (~b(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10531, 10524])).
% 2.74/2.92 tff(10533,plain,
% 2.74/2.92 (r(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[157, 10532])).
% 2.74/2.92 tff(10534,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10410, 106, 10533, 10469, 10467])).
% 2.74/2.92 tff(10535,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[205, 10534])).
% 2.74/2.92 tff(10536,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10537,plain,
% 2.74/2.92 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10538,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[10537])).
% 2.74/2.92 tff(10539,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[10538, 10536])).
% 2.74/2.92 tff(10540,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(10541,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[10540, 10539])).
% 2.74/2.92 tff(10542,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10541, 171, 10487, 10535, 10465, 10463])).
% 2.74/2.92 tff(10543,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10544,plain,
% 2.74/2.92 (~r(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10543, 4, 126])).
% 2.74/2.92 tff(10545,plain,
% 2.74/2.92 (b(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[244, 10544])).
% 2.74/2.92 tff(10546,plain,
% 2.74/2.92 ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3289, 9835])).
% 2.74/2.92 tff(10547,plain,
% 2.74/2.92 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10546, 10545, 10228, 4])).
% 2.74/2.92 tff(10548,plain,
% 2.74/2.92 ((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3256, 9835])).
% 2.74/2.92 tff(10549,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10548, 10545, 126, 10422, 10467])).
% 2.74/2.92 tff(10550,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[225, 10549, 10547])).
% 2.74/2.92 tff(10551,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10552,plain,
% 2.74/2.92 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10551, 126])).
% 2.74/2.92 tff(10553,plain,
% 2.74/2.92 (r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[479, 10552])).
% 2.74/2.92 tff(10554,plain,
% 2.74/2.92 ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5764, 355])).
% 2.74/2.92 tff(10555,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10554, 2, 126, 10553])).
% 2.74/2.92 tff(10556,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9955, 10555])).
% 2.74/2.92 tff(10557,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9352, 2, 10422, 10553])).
% 2.74/2.92 tff(10558,plain,
% 2.74/2.92 (b(s(s(s(z))), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[1173, 10557])).
% 2.74/2.92 tff(10559,plain,
% 2.74/2.92 (~b(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10424, 10558, 10228])).
% 2.74/2.92 tff(10560,plain,
% 2.74/2.92 (r(s(s(s(z))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10429, 10559])).
% 2.74/2.92 tff(10561,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 2.74/2.92 tff(10562,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9616, 171, 3281, 9835, 357])).
% 2.74/2.92 tff(10563,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[274, 10562])).
% 2.74/2.92 tff(10564,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10565,plain,
% 2.74/2.92 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10566,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[10565])).
% 2.74/2.92 tff(10567,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[10566, 10564])).
% 2.74/2.92 tff(10568,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(10569,plain,
% 2.74/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[10568, 10567])).
% 2.74/2.92 tff(10570,plain,
% 2.74/2.92 (~b(z, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10569, 171, 3281, 9835, 357])).
% 2.74/2.92 tff(10571,plain,
% 2.74/2.92 (r(z, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[293, 10570])).
% 2.74/2.92 tff(10572,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10573,plain,
% 2.74/2.92 (((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10574,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[10573])).
% 2.74/2.92 tff(10575,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.92 inference(transitivity,[status(thm)],[10574, 10572])).
% 2.74/2.92 tff(10576,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(10577,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[10576, 10575])).
% 2.74/2.92 tff(10578,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10577, 106, 10571, 2828, 10563, 10561])).
% 2.74/2.92 tff(10579,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10580,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10579, 10560, 10228, 10556])).
% 2.74/2.92 tff(10581,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10361, 10580])).
% 2.74/2.92 tff(10582,plain,
% 2.74/2.92 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[8545, 10581, 10558, 10556])).
% 2.74/2.92 tff(10583,plain,
% 2.74/2.92 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9990, 10582])).
% 2.74/2.92 tff(10584,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[6169, 10553, 126, 10422])).
% 2.74/2.92 tff(10585,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[205, 10584])).
% 2.74/2.92 tff(10586,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9616, 171, 10228, 9835, 10556])).
% 2.74/2.92 tff(10587,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[274, 10586])).
% 2.74/2.92 tff(10588,plain,
% 2.74/2.92 (~b(z, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10569, 171, 10228, 9835, 10556])).
% 2.74/2.92 tff(10589,plain,
% 2.74/2.92 (r(z, s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[293, 10588])).
% 2.74/2.92 tff(10590,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7068, 260, 502, 3])).
% 2.74/2.92 tff(10591,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[427, 10590])).
% 2.74/2.92 tff(10592,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5971, 260, 2, 3])).
% 2.74/2.92 tff(10593,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[351, 10592])).
% 2.74/2.92 tff(10594,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10084, 10593, 10591, 1, 207, 357])).
% 2.74/2.92 tff(10595,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10596,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10595, 1, 207, 357, 2, 3, 502])).
% 2.74/2.92 tff(10597,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3668, 10596])).
% 2.74/2.92 tff(10598,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5760, 10597, 160, 207])).
% 2.74/2.92 tff(10599,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9958, 10598])).
% 2.74/2.92 tff(10600,plain,
% 2.74/2.92 ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z)))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5797, 355])).
% 2.74/2.92 tff(10601,plain,
% 2.74/2.92 (~b(z, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10600, 10597, 2, 160, 207])).
% 2.74/2.92 tff(10602,plain,
% 2.74/2.92 (r(z, s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[498, 10601])).
% 2.74/2.92 tff(10603,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[7972, 10602, 5567, 10599])).
% 2.74/2.92 tff(10604,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[427, 10603])).
% 2.74/2.92 tff(10605,plain,
% 2.74/2.92 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10120, 10599, 3, 554])).
% 2.74/2.92 tff(10606,plain,
% 2.74/2.92 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[351, 10605])).
% 2.74/2.92 tff(10607,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10084, 10606, 10604, 1, 207, 357])).
% 2.74/2.92 tff(10608,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10609,plain,
% 2.74/2.92 (~b(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10608, 10465, 10556, 10583, 10422, 10589, 10585, 2, 10553])).
% 2.74/2.92 tff(10610,plain,
% 2.74/2.92 (r(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[157, 10609])).
% 2.74/2.92 tff(10611,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10612,plain,
% 2.74/2.92 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(rewrite,[status(thm)],[])).
% 2.74/2.92 tff(10613,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))))),
% 2.74/2.92 inference(monotonicity,[status(thm)],[10612])).
% 2.74/2.92 tff(10614,plain,
% 2.74/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.92 inference(transitivity,[status(thm)],[10613, 10611])).
% 2.74/2.92 tff(10615,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.92 inference(quant_inst,[status(thm)],[])).
% 2.74/2.92 tff(10616,plain,
% 2.74/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(z))))))),
% 2.74/2.92 inference(modus_ponens,[status(thm)],[10615, 10614])).
% 2.74/2.92 tff(10617,plain,
% 2.74/2.92 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10616, 106, 10610, 10589, 10587])).
% 2.74/2.92 tff(10618,plain,
% 2.74/2.92 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9958, 10617])).
% 2.74/2.92 tff(10619,plain,
% 2.74/2.92 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[5760, 10618, 10585, 10465])).
% 2.74/2.92 tff(10620,plain,
% 2.74/2.92 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3668, 10619])).
% 2.74/2.92 tff(10621,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[534, 106, 10620, 126, 10553, 10583])).
% 2.74/2.92 tff(10622,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10623,plain,
% 2.74/2.92 (~r(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10622, 126])).
% 2.74/2.92 tff(10624,plain,
% 2.74/2.92 (b(s(s(z)), s(z))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[244, 10623])).
% 2.74/2.92 tff(10625,plain,
% 2.74/2.92 (~b(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3205, 171, 10228, 10624, 9835])).
% 2.74/2.92 tff(10626,plain,
% 2.74/2.92 (r(s(s(z)), z)),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[157, 10625])).
% 2.74/2.92 tff(10627,plain,
% 2.74/2.92 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[3167, 10626, 126, 10422])).
% 2.74/2.92 tff(10628,plain,
% 2.74/2.92 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[225, 10627])).
% 2.74/2.92 tff(10629,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10370, 1998, 10553, 126])).
% 2.74/2.92 tff(10630,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2614, 10629])).
% 2.74/2.92 tff(10631,plain,
% 2.74/2.92 ($false),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[9271, 106, 554, 637, 1199, 1998])).
% 2.74/2.92 tff(10632,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.92 tff(10633,plain,
% 2.74/2.92 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[10632, 1998, 10422, 10626])).
% 2.74/2.92 tff(10634,plain,
% 2.74/2.92 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.92 inference(unit_resolution,[status(thm)],[2642, 10633])).
% 2.74/2.92 tff(10635,plain,
% 2.74/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10636,plain,
% 2.74/2.93 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10637,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[10636])).
% 2.74/2.93 tff(10638,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[10637, 10635])).
% 2.74/2.93 tff(10639,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(10640,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[10639, 10638])).
% 2.74/2.93 tff(10641,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10640, 171, 10624, 10634, 10630, 10585, 10628])).
% 2.74/2.93 tff(10642,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10643,plain,
% 2.74/2.93 (~r(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10642, 126])).
% 2.74/2.93 tff(10644,plain,
% 2.74/2.93 (b(s(z), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1996, 10643])).
% 2.74/2.93 tff(10645,plain,
% 2.74/2.93 (~b(s(s(z)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3205, 171, 3281, 259, 9835])).
% 2.74/2.93 tff(10646,plain,
% 2.74/2.93 (r(s(s(z)), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[157, 10645])).
% 2.74/2.93 tff(10647,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10648,plain,
% 2.74/2.93 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10649,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[10648])).
% 2.74/2.93 tff(10650,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[10649, 10647])).
% 2.74/2.93 tff(10651,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(10652,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(z, s(s(z))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[10651, 10650])).
% 2.74/2.93 tff(10653,plain,
% 2.74/2.93 (~b(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10652, 171, 3281, 259, 9835])).
% 2.74/2.93 tff(10654,plain,
% 2.74/2.93 (r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[124, 10653])).
% 2.74/2.93 tff(10655,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3707, 10324, 10654, 10646])).
% 2.74/2.93 tff(10656,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[274, 10655])).
% 2.74/2.93 tff(10657,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9616, 171, 3281, 9835, 357, 10656])).
% 2.74/2.93 tff(10658,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10659,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10658, 10228, 10624])).
% 2.74/2.93 tff(10660,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9955, 10659])).
% 2.74/2.93 tff(10661,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10337, 10660, 10553, 126])).
% 2.74/2.93 tff(10662,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3668, 10661])).
% 2.74/2.93 tff(10663,plain,
% 2.74/2.93 (~b(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10652, 171, 10228, 10624, 9835])).
% 2.74/2.93 tff(10664,plain,
% 2.74/2.93 (r(z, s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[124, 10663])).
% 2.74/2.93 tff(10665,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[5760, 10662, 10585, 10628])).
% 2.74/2.93 tff(10666,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9958, 10665])).
% 2.74/2.93 tff(10667,plain,
% 2.74/2.93 (~r(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[6247, 10666, 10664, 10626])).
% 2.74/2.93 tff(10668,plain,
% 2.74/2.93 (b(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[293, 10667])).
% 2.74/2.93 tff(10669,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8284, 10644, 10228, 10624])).
% 2.74/2.93 tff(10670,plain,
% 2.74/2.93 (r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1173, 10669])).
% 2.74/2.93 tff(10671,plain,
% 2.74/2.93 (~r(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8249, 10670, 10553, 10662])).
% 2.74/2.93 tff(10672,plain,
% 2.74/2.93 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9990, 10671])).
% 2.74/2.93 tff(10673,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10674,plain,
% 2.74/2.93 (((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10675,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[10674])).
% 2.74/2.93 tff(10676,plain,
% 2.74/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[10675, 10673])).
% 2.74/2.93 tff(10677,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(10678,plain,
% 2.74/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z)))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[10677, 10676])).
% 2.74/2.93 tff(10679,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10678, 106, 126, 1357, 502, 747])).
% 2.74/2.93 tff(10680,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10681,plain,
% 2.74/2.93 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10680, 10670, 10553, 126])).
% 2.74/2.93 tff(10682,plain,
% 2.74/2.93 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1368, 10681])).
% 2.74/2.93 tff(10683,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10684,plain,
% 2.74/2.93 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10685,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[10684])).
% 2.74/2.93 tff(10686,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.93 inference(transitivity,[status(thm)],[10685, 10683])).
% 2.74/2.93 tff(10687,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(10688,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 2.74/2.93 tff(10689,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10688, 171, 3281, 3686, 1976, 1384, 376, 2527])).
% 2.74/2.93 tff(10690,plain,((~b(z, s(s(s(s(z)))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10691,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10690, 10682, 10672, 10668, 10662, 10644, 10228])).
% 2.74/2.93 tff(10692,plain,(~r(s(z), s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10693,plain,
% 2.74/2.93 (b(s(z), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[60, 10692])).
% 2.74/2.93 tff(10694,plain,
% 2.74/2.93 ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[8383, 9835])).
% 2.74/2.93 tff(10695,plain,
% 2.74/2.93 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10694, 3281, 10693])).
% 2.74/2.93 tff(10696,plain,
% 2.74/2.93 (r(s(s(s(s(s(z))))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[145, 10695])).
% 2.74/2.93 tff(10697,plain,
% 2.74/2.93 (~b(s(s(z)), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10658, 357, 3281])).
% 2.74/2.93 tff(10698,plain,
% 2.74/2.93 (r(s(s(z)), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[244, 10697])).
% 2.74/2.93 tff(10699,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9676, 357, 10693, 3281])).
% 2.74/2.93 tff(10700,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3668, 10699])).
% 2.74/2.93 tff(10701,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9418, 106, 260, 10696, 9843])).
% 2.74/2.93 tff(10702,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[274, 10701])).
% 2.74/2.93 tff(10703,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10704,plain,
% 2.74/2.93 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.93 inference(rewrite,[status(thm)],[])).
% 2.74/2.93 tff(10705,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.74/2.93 inference(monotonicity,[status(thm)],[10704])).
% 2.74/2.93 tff(10706,plain,
% 2.74/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.93 inference(transitivity,[status(thm)],[10705, 10703])).
% 2.74/2.93 tff(10707,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/2.93 inference(quant_inst,[status(thm)],[])).
% 2.74/2.93 tff(10708,plain,
% 2.74/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.74/2.93 inference(modus_ponens,[status(thm)],[10707, 10706])).
% 2.74/2.93 tff(10709,plain,
% 2.74/2.93 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10708, 171, 3281, 9835, 10702])).
% 2.74/2.93 tff(10710,plain,
% 2.74/2.93 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9990, 10709])).
% 2.74/2.93 tff(10711,plain,
% 2.74/2.93 (~b(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10448, 4, 3281])).
% 2.74/2.93 tff(10712,plain,
% 2.74/2.93 (r(s(s(s(z))), s(z))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[1173, 10711])).
% 2.74/2.93 tff(10713,plain,
% 2.74/2.93 (~r(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9141, 10712, 1998, 6477])).
% 2.74/2.93 tff(10714,plain,
% 2.74/2.93 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9990, 10713])).
% 2.74/2.93 tff(10715,plain,
% 2.74/2.93 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9808, 10714, 10693, 4])).
% 2.74/2.93 tff(10716,plain,
% 2.74/2.93 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[3668, 10715])).
% 2.74/2.93 tff(10717,plain,
% 2.74/2.93 (~r(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9418, 106, 10716, 10696, 9843])).
% 2.74/2.93 tff(10718,plain,
% 2.74/2.93 (b(s(s(s(s(z)))), z)),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[274, 10717])).
% 2.74/2.93 tff(10719,plain,
% 2.74/2.93 (~r(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[9423, 106, 10716, 10696, 9843])).
% 2.74/2.93 tff(10720,plain,
% 2.74/2.93 (b(z, s(s(s(s(z)))))),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[293, 10719])).
% 2.74/2.93 tff(10721,plain,
% 2.74/2.93 ($false),
% 2.74/2.93 inference(unit_resolution,[status(thm)],[10202, 171, 9835, 10714, 10720, 10718])).
% 2.74/2.93 tff(10722,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.93 tff(10723,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10722, 6477, 1998, 3281])).
% 2.74/2.94 tff(10724,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[479, 10723])).
% 2.74/2.94 tff(10725,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9141, 3, 1998, 6477])).
% 2.74/2.94 tff(10726,plain,
% 2.74/2.94 (b(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1173, 10725])).
% 2.74/2.94 tff(10727,plain,
% 2.74/2.94 (~b(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10424, 10726, 3281])).
% 2.74/2.94 tff(10728,plain,
% 2.74/2.94 (r(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10429, 10727])).
% 2.74/2.94 tff(10729,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10730,plain,
% 2.74/2.94 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10731,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10730])).
% 2.74/2.94 tff(10732,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[10731, 10729])).
% 2.74/2.94 tff(10733,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10734,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10733, 10732])).
% 2.74/2.94 tff(10735,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10734, 106, 1998, 3, 6477, 10728])).
% 2.74/2.94 tff(10736,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(10737,plain,
% 2.74/2.94 (~r(s(z), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10736, 6477, 1998, 3281])).
% 2.74/2.94 tff(10738,plain,
% 2.74/2.94 (b(s(z), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9990, 10737])).
% 2.74/2.94 tff(10739,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[8521, 3686, 10693, 10738])).
% 2.74/2.94 tff(10740,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[427, 10739])).
% 2.74/2.94 tff(10741,plain,
% 2.74/2.94 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9676, 3686, 10693, 3281])).
% 2.74/2.94 tff(10742,plain,
% 2.74/2.94 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[9955, 10741])).
% 2.74/2.94 tff(10743,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[6485, 10742, 1998, 6477])).
% 2.74/2.94 tff(10744,plain,
% 2.74/2.94 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2614, 10743])).
% 2.74/2.94 tff(10745,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10746,plain,
% 2.74/2.94 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10747,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10746])).
% 2.74/2.94 tff(10748,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[10747, 10745])).
% 2.74/2.94 tff(10749,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10750,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10749, 10748])).
% 2.74/2.94 tff(10751,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10750, 171, 3686, 838, 1275, 1384, 376])).
% 2.74/2.94 tff(10752,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(10753,plain,
% 2.74/2.94 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10752, 10744, 10693, 10738, 3686])).
% 2.74/2.94 tff(10754,plain,
% 2.74/2.94 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1368, 10753])).
% 2.74/2.94 tff(10755,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[8843, 10754, 6477, 10740])).
% 2.74/2.94 tff(10756,plain,
% 2.74/2.94 (b(s(s(s(z))), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[1173, 10755])).
% 2.74/2.94 tff(10757,plain,
% 2.74/2.94 (~r(s(z), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[7054, 10742, 10740, 10724])).
% 2.74/2.94 tff(10758,plain,
% 2.74/2.94 (b(s(z), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[550, 10757])).
% 2.74/2.94 tff(10759,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10760,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10761,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10760, 10759])).
% 2.74/2.94 tff(10762,plain,
% 2.74/2.94 ($false),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10761, 106, 5609, 1357, 1199, 6477])).
% 2.74/2.94 tff(10763,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.94 tff(10764,plain,
% 2.74/2.94 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10763, 10754, 6477, 10740])).
% 2.74/2.94 tff(10765,plain,
% 2.74/2.94 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2642, 10764])).
% 2.74/2.94 tff(10766,plain,
% 2.74/2.94 (~b(s(s(z)), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[2707, 10765, 10756, 10758])).
% 2.74/2.94 tff(10767,plain,
% 2.74/2.94 (r(s(s(z)), s(z))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[244, 10766])).
% 2.74/2.94 tff(10768,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10769,plain,
% 2.74/2.94 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10770,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10769])).
% 2.74/2.94 tff(10771,plain,
% 2.74/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[10770, 10768])).
% 2.74/2.94 tff(10772,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10773,plain,
% 2.74/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10772, 10771])).
% 2.74/2.94 tff(10774,plain,
% 2.74/2.94 (~b(z, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10773, 171, 3281, 3133, 1188])).
% 2.74/2.94 tff(10775,plain,
% 2.74/2.94 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[8373, 25, 10774])).
% 2.74/2.94 tff(10776,plain,
% 2.74/2.94 (r(z, s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10775, 8359])).
% 2.74/2.94 tff(10777,plain,
% 2.74/2.94 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[353])).
% 2.74/2.94 tff(10778,plain,
% 2.74/2.94 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10777])).
% 2.74/2.94 tff(10779,plain,
% 2.74/2.94 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[369, 10778])).
% 2.74/2.94 tff(10780,plain,
% 2.74/2.94 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.74/2.94 inference(symmetry,[status(thm)],[1125])).
% 2.74/2.94 tff(10781,plain,
% 2.74/2.94 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10780])).
% 2.74/2.94 tff(10782,plain,
% 2.74/2.94 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[2839, 10781])).
% 2.74/2.94 tff(10783,plain,
% 2.74/2.94 (~b(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10291, 171, 3281, 3133, 1188])).
% 2.74/2.94 tff(10784,plain,
% 2.74/2.94 (r(s(s(s(z))), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[953, 25, 194, 10783])).
% 2.74/2.94 tff(10785,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10786,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10787,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10786, 10785])).
% 2.74/2.94 tff(10788,plain,
% 2.74/2.94 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10787, 106, 2118, 10784, 10776])).
% 2.74/2.94 tff(10789,plain,
% 2.74/2.94 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[4240, 25, 10788])).
% 2.74/2.94 tff(10790,plain,
% 2.74/2.94 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10789, 10782])).
% 2.74/2.94 tff(10791,plain,
% 2.74/2.94 (~b(s(s(z)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10236, 323, 3133, 3281])).
% 2.74/2.94 tff(10792,plain,
% 2.74/2.94 (r(s(s(z)), z)),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[157, 10791])).
% 2.74/2.94 tff(10793,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10794,plain,
% 2.74/2.94 (((~r(z, s(s(s(z))))) | (~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(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10795,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10794])).
% 2.74/2.94 tff(10796,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.94 inference(transitivity,[status(thm)],[10795, 10793])).
% 2.74/2.94 tff(10797,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10798,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10797, 10796])).
% 2.74/2.94 tff(10799,plain,
% 2.74/2.94 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10798, 106, 10792, 2118, 10776])).
% 2.74/2.94 tff(10800,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[349, 25, 10799])).
% 2.74/2.94 tff(10801,plain,
% 2.74/2.94 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10800, 10779])).
% 2.74/2.94 tff(10802,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10803,plain,
% 2.74/2.94 (((~r(z, s(s(s(z))))) | (~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(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(rewrite,[status(thm)],[])).
% 2.74/2.94 tff(10804,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))) | (~r(s(s(s(z))), z))))),
% 2.74/2.94 inference(monotonicity,[status(thm)],[10803])).
% 2.74/2.94 tff(10805,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.94 inference(transitivity,[status(thm)],[10804, 10802])).
% 2.74/2.94 tff(10806,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.74/2.94 inference(quant_inst,[status(thm)],[])).
% 2.74/2.94 tff(10807,plain,
% 2.74/2.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))) | (~r(s(s(s(z))), z))),
% 2.74/2.94 inference(modus_ponens,[status(thm)],[10806, 10805])).
% 2.74/2.94 tff(10808,plain,
% 2.74/2.94 (~r(s(s(z)), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10807, 106, 10792, 10784, 10776])).
% 2.74/2.94 tff(10809,plain,
% 2.74/2.94 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[979, 25, 10808])).
% 2.74/2.94 tff(10810,plain,
% 2.74/2.94 (b(s(s(z)), s(s(s(z))))),
% 2.74/2.94 inference(unit_resolution,[status(thm)],[10809, 900])).
% 2.74/2.94 tff(10811,plain,
% 2.74/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10812,plain,
% 2.74/2.95 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10813,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10812])).
% 2.74/2.95 tff(10814,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10813, 10811])).
% 2.74/2.95 tff(10815,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10816,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10815, 10814])).
% 2.74/2.95 tff(10817,plain,
% 2.74/2.95 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10816, 106, 10792, 2118, 10776])).
% 2.74/2.95 tff(10818,plain,
% 2.74/2.95 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[374, 10817, 369])).
% 2.74/2.95 tff(10819,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10820,plain,
% 2.74/2.95 (((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10821,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10820])).
% 2.74/2.95 tff(10822,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), 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))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10821, 10819])).
% 2.74/2.95 tff(10823,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10824,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10823, 10822])).
% 2.74/2.95 tff(10825,plain,
% 2.74/2.95 ($false),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10824, 171, 323, 1188, 6462, 10818, 10810, 10801])).
% 2.74/2.95 tff(10826,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.95 tff(10827,plain,
% 2.74/2.95 (~b(s(z), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10826, 1188, 10790, 369, 2118, 3133, 3281])).
% 2.74/2.95 tff(10828,plain,
% 2.74/2.95 (r(s(z), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[550, 10827])).
% 2.74/2.95 tff(10829,plain,
% 2.74/2.95 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[9443, 106, 10828, 2, 263])).
% 2.74/2.95 tff(10830,plain,
% 2.74/2.95 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[349, 25, 10829])).
% 2.74/2.95 tff(10831,plain,
% 2.74/2.95 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10830, 10779])).
% 2.74/2.95 tff(10832,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10833,plain,
% 2.74/2.95 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10834,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10833])).
% 2.74/2.95 tff(10835,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10834, 10832])).
% 2.74/2.95 tff(10836,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10837,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10836, 10835])).
% 2.74/2.95 tff(10838,plain,
% 2.74/2.95 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10837, 106, 2118, 10784, 10776])).
% 2.74/2.95 tff(10839,plain,
% 2.74/2.95 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2842, 10838, 2839])).
% 2.74/2.95 tff(10840,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10841,plain,
% 2.74/2.95 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10842,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10841])).
% 2.74/2.95 tff(10843,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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)))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10842, 10840])).
% 2.74/2.95 tff(10844,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10845,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(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))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10844, 10843])).
% 2.74/2.95 tff(10846,plain,
% 2.74/2.95 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10845, 171, 1188, 10790, 10839, 10831])).
% 2.74/2.95 tff(10847,plain,
% 2.74/2.95 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[979, 25, 10846])).
% 2.74/2.95 tff(10848,plain,
% 2.74/2.95 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10847, 900])).
% 2.74/2.95 tff(10849,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10850,plain,
% 2.74/2.95 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(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(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)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10851,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10850])).
% 2.74/2.95 tff(10852,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10851, 10849])).
% 2.74/2.95 tff(10853,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10854,plain,
% 2.74/2.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10853, 10852])).
% 2.74/2.95 tff(10855,plain,
% 2.74/2.95 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10854, 171, 10790, 10839, 10831])).
% 2.74/2.95 tff(10856,plain,
% 2.74/2.95 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[2640, 25, 10855, 80])).
% 2.74/2.95 tff(10857,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10858,plain,
% 2.74/2.95 (((~r(s(s(s(z))), s(s(z)))) | (~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(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10859,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 2.74/2.95 inference(monotonicity,[status(thm)],[10858])).
% 2.74/2.95 tff(10860,plain,
% 2.74/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.95 inference(transitivity,[status(thm)],[10859, 10857])).
% 2.74/2.95 tff(10861,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.74/2.95 inference(quant_inst,[status(thm)],[])).
% 2.74/2.95 tff(10862,plain,
% 2.74/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))),
% 2.74/2.95 inference(modus_ponens,[status(thm)],[10861, 10860])).
% 2.74/2.95 tff(10863,plain,
% 2.74/2.95 (~r(s(s(z)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[10862, 106, 10856, 10848, 10776])).
% 2.74/2.95 tff(10864,plain,
% 2.74/2.95 (b(s(s(z)), z)),
% 2.74/2.95 inference(unit_resolution,[status(thm)],[157, 10863])).
% 2.74/2.95 tff(10865,plain,
% 2.74/2.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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)))))))),
% 2.74/2.95 inference(rewrite,[status(thm)],[])).
% 2.74/2.95 tff(10866,plain,
% 2.74/2.95 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), 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(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10867,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10866])).
% 2.74/2.96 tff(10868,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[10867, 10865])).
% 2.74/2.96 tff(10869,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10870,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(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))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10869, 10868])).
% 2.74/2.96 tff(10871,plain,
% 2.74/2.96 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10870, 171, 3281, 1188, 10790, 10831])).
% 2.74/2.96 tff(10872,plain,
% 2.74/2.96 (~b(z, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10871, 10864])).
% 2.74/2.96 tff(10873,plain,
% 2.74/2.96 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[291, 25, 10872])).
% 2.74/2.96 tff(10874,plain,
% 2.74/2.96 (r(z, s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10873, 5641])).
% 2.74/2.96 tff(10875,assumption,(~(s(s(s(s(s(z))))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.74/2.96 tff(10876,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10877,plain,
% 2.74/2.96 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10878,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10877])).
% 2.74/2.96 tff(10879,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[10878, 10876])).
% 2.74/2.96 tff(10880,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10881,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10880, 10879])).
% 2.74/2.96 tff(10882,plain,
% 2.74/2.96 (~r(z, s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10881, 106, 10856, 10848, 10776])).
% 2.74/2.96 tff(10883,plain,
% 2.74/2.96 (b(z, s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[124, 10882])).
% 2.74/2.96 tff(10884,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10885,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10886,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10885, 10884])).
% 2.74/2.96 tff(10887,plain,
% 2.74/2.96 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10886, 106, 10828, 2, 263])).
% 2.74/2.96 tff(10888,plain,
% 2.74/2.96 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[374, 10887, 369])).
% 2.74/2.96 tff(10889,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(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(z))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10890,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(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(z))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10891,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10890, 10889])).
% 2.74/2.96 tff(10892,plain,
% 2.74/2.96 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10891, 106, 2, 1199, 396])).
% 2.74/2.96 tff(10893,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[9332, 106, 554, 2, 502, 396])).
% 2.74/2.96 tff(10894,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(10895,plain,
% 2.74/2.96 (~r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10894, 396, 2, 554])).
% 2.74/2.96 tff(10896,plain,
% 2.74/2.96 (b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[479, 10895])).
% 2.74/2.96 tff(10897,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10898,plain,
% 2.74/2.96 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10899,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10898])).
% 2.74/2.96 tff(10900,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[10899, 10897])).
% 2.74/2.96 tff(10901,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10902,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10901, 10900])).
% 2.74/2.96 tff(10903,plain,
% 2.74/2.96 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10902, 171, 3281, 3133, 1188, 10896])).
% 2.74/2.96 tff(10904,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[1368, 10903, 10892])).
% 2.74/2.96 tff(10905,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(10906,plain,
% 2.74/2.96 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10905, 1188, 3133, 3281, 2, 10856, 10828])).
% 2.74/2.96 tff(10907,plain,
% 2.74/2.96 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[225, 10906])).
% 2.74/2.96 tff(10908,plain,
% 2.74/2.96 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[634, 10907, 10888, 10883, 10864])).
% 2.74/2.96 tff(10909,plain,
% 2.74/2.96 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[426, 10908, 10875])).
% 2.74/2.96 tff(10910,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10911,plain,
% 2.74/2.96 (((~r(s(s(s(s(z)))), s(z))) | (~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(z)))), s(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)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10912,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10911])).
% 2.74/2.96 tff(10913,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.96 inference(transitivity,[status(thm)],[10912, 10910])).
% 2.74/2.96 tff(10914,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~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)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10915,plain,
% 2.74/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10914, 10913])).
% 2.74/2.96 tff(10916,plain,
% 2.74/2.96 (~r(s(s(s(s(s(z))))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10915, 106, 10909, 10874, 263])).
% 2.74/2.96 tff(10917,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10918,plain,
% 2.74/2.96 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10919,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10918])).
% 2.74/2.96 tff(10920,plain,
% 2.74/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.74/2.96 inference(transitivity,[status(thm)],[10919, 10917])).
% 2.74/2.96 tff(10921,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.74/2.96 inference(quant_inst,[status(thm)],[])).
% 2.74/2.96 tff(10922,plain,
% 2.74/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), z))),
% 2.74/2.96 inference(modus_ponens,[status(thm)],[10921, 10920])).
% 2.74/2.96 tff(10923,plain,
% 2.74/2.96 (~b(s(s(s(s(s(z))))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10922, 171, 3281, 10883, 10864, 10907])).
% 2.74/2.96 tff(10924,plain,
% 2.74/2.96 ($false),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[143, 25, 140, 10923, 10916])).
% 2.74/2.96 tff(10925,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.96 tff(10926,plain,
% 2.74/2.96 ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(s(s(s(z)))), z)) | (s(s(s(z))) = s(s(s(s(z)))))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10925, 422])).
% 2.74/2.96 tff(10927,plain,
% 2.74/2.96 ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), z))),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10926, 2264, 9835, 355])).
% 2.74/2.96 tff(10928,plain,
% 2.74/2.96 (~r(s(s(s(s(z)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[10927, 10767, 3281, 10742, 10756])).
% 2.74/2.96 tff(10929,plain,
% 2.74/2.96 (b(s(s(s(s(z)))), z)),
% 2.74/2.96 inference(unit_resolution,[status(thm)],[274, 10928])).
% 2.74/2.96 tff(10930,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10931,plain,
% 2.74/2.96 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(z)))), s(s(s(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)))))))),
% 2.74/2.96 inference(rewrite,[status(thm)],[])).
% 2.74/2.96 tff(10932,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 2.74/2.96 inference(monotonicity,[status(thm)],[10931])).
% 2.74/2.96 tff(10933,plain,
% 2.74/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[10932, 10930])).
% 2.74/2.97 tff(10934,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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)))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(10935,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[10934, 10933])).
% 2.74/2.97 tff(10936,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10935, 106, 5609, 5567, 6477, 127])).
% 2.74/2.97 tff(10937,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(10938,plain,
% 2.74/2.97 (~r(z, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10937, 10740, 6477, 10696])).
% 2.74/2.97 tff(10939,plain,
% 2.74/2.97 (b(z, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[293, 10938])).
% 2.74/2.97 tff(10940,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10351, 171, 9835, 3686, 10738, 10939, 10929])).
% 2.74/2.97 tff(10941,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(10942,plain,
% 2.74/2.97 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10941, 6477, 3281, 1998])).
% 2.74/2.97 tff(10943,plain,
% 2.74/2.97 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[3668, 10942])).
% 2.74/2.97 tff(10944,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2312, 10943, 1998, 10724])).
% 2.74/2.97 tff(10945,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9955, 10944])).
% 2.74/2.97 tff(10946,plain,
% 2.74/2.97 (~b(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10658, 10945, 3281])).
% 2.74/2.97 tff(10947,plain,
% 2.74/2.97 (r(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[244, 10946])).
% 2.74/2.97 tff(10948,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10949,plain,
% 2.74/2.97 (((~r(s(z), s(s(s(z))))) | (~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))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10950,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[10949])).
% 2.74/2.97 tff(10951,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[10950, 10948])).
% 2.74/2.97 tff(10952,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(10953,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[10952, 10951])).
% 2.74/2.97 tff(10954,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10953, 106, 2, 502, 1998, 396])).
% 2.74/2.97 tff(10955,plain,((~r(s(z), s(s(s(z))))) | (~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))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(10956,plain,
% 2.74/2.97 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10955, 10947, 1998, 10724])).
% 2.74/2.97 tff(10957,plain,
% 2.74/2.97 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[225, 10956])).
% 2.74/2.97 tff(10958,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10959,plain,
% 2.74/2.97 (((~r(s(z), s(s(s(z))))) | (~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)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10960,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[10959])).
% 2.74/2.97 tff(10961,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[10960, 10958])).
% 2.74/2.97 tff(10962,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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))))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(10963,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[10962, 10961])).
% 2.74/2.97 tff(10964,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10963, 106, 10947, 10724, 1998])).
% 2.74/2.97 tff(10965,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[205, 10964])).
% 2.74/2.97 tff(10966,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9195, 10943, 6477, 10724])).
% 2.74/2.97 tff(10967,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2614, 10966])).
% 2.74/2.97 tff(10968,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10246, 171, 10967, 10965, 10957])).
% 2.74/2.97 tff(10969,plain,
% 2.74/2.97 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2642, 10968])).
% 2.74/2.97 tff(10970,plain,
% 2.74/2.97 (~b(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8497, 171, 10693, 10965, 10957])).
% 2.74/2.97 tff(10971,plain,
% 2.74/2.97 (r(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[550, 10970])).
% 2.74/2.97 tff(10972,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8788, 10971, 10969, 1998, 10947])).
% 2.74/2.97 tff(10973,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(10974,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10973, 3281, 1998])).
% 2.74/2.97 tff(10975,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6475, 10974])).
% 2.74/2.97 tff(10976,plain,
% 2.74/2.97 (~r(z, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9423, 106, 260, 10696, 9843])).
% 2.74/2.97 tff(10977,plain,
% 2.74/2.97 (b(z, s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[293, 10976])).
% 2.74/2.97 tff(10978,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10070, 554, 10710, 260])).
% 2.74/2.97 tff(10979,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[351, 10978])).
% 2.74/2.97 tff(10980,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[6470, 10979, 10977, 10975, 10702])).
% 2.74/2.97 tff(10981,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[157, 10980])).
% 2.74/2.97 tff(10982,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10632, 10981, 1998, 554])).
% 2.74/2.97 tff(10983,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2642, 10982])).
% 2.74/2.97 tff(10984,plain,
% 2.74/2.97 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10985,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[10984])).
% 2.74/2.97 tff(10986,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.74/2.97 inference(transitivity,[status(thm)],[10985, 9611])).
% 2.74/2.97 tff(10987,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(10988,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[10987, 10986])).
% 2.74/2.97 tff(10989,plain,
% 2.74/2.97 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10988, 171, 3281, 9835, 10702])).
% 2.74/2.97 tff(10990,plain,
% 2.74/2.97 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9955, 10989])).
% 2.74/2.97 tff(10991,plain,
% 2.74/2.97 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10398, 10981, 3281, 4])).
% 2.74/2.97 tff(10992,plain,
% 2.74/2.97 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[225, 10991])).
% 2.74/2.97 tff(10993,plain,
% 2.74/2.97 (~b(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10546, 10992, 3281, 4])).
% 2.74/2.97 tff(10994,plain,
% 2.74/2.97 (r(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[244, 10993])).
% 2.74/2.97 tff(10995,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10996,plain,
% 2.74/2.97 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(10997,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[10996])).
% 2.74/2.97 tff(10998,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[10997, 10995])).
% 2.74/2.97 tff(10999,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(11000,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[10999, 10998])).
% 2.74/2.97 tff(11001,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11000, 106, 2, 1998, 263, 569])).
% 2.74/2.97 tff(11002,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(11003,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11002, 10994, 1998, 10990])).
% 2.74/2.97 tff(11004,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9958, 11003])).
% 2.74/2.97 tff(11005,plain,
% 2.74/2.97 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8894, 11004, 10975, 10983])).
% 2.74/2.97 tff(11006,plain,
% 2.74/2.97 ($false),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9326, 106, 554, 10994, 10712, 11005])).
% 2.74/2.97 tff(11007,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.97 tff(11008,plain,
% 2.74/2.97 (~r(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11007, 260, 3281, 4, 1998])).
% 2.74/2.97 tff(11009,plain,
% 2.74/2.97 (b(s(z), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[550, 11008])).
% 2.74/2.97 tff(11010,plain,
% 2.74/2.97 (~b(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10237, 11009, 3281])).
% 2.74/2.97 tff(11011,plain,
% 2.74/2.97 (r(s(s(z)), z)),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[157, 11010])).
% 2.74/2.97 tff(11012,plain,
% 2.74/2.97 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10398, 11011, 3281, 4])).
% 2.74/2.97 tff(11013,plain,
% 2.74/2.97 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[225, 11012])).
% 2.74/2.97 tff(11014,plain,
% 2.74/2.97 (~b(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10546, 11013, 3281, 4])).
% 2.74/2.97 tff(11015,plain,
% 2.74/2.97 (r(s(s(z)), s(z))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[244, 11014])).
% 2.74/2.97 tff(11016,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5971, 11015, 10710, 260])).
% 2.74/2.97 tff(11017,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[351, 11016])).
% 2.74/2.97 tff(11018,plain,
% 2.74/2.97 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11002, 11015, 1998, 10990])).
% 2.74/2.97 tff(11019,plain,
% 2.74/2.97 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9958, 11018])).
% 2.74/2.97 tff(11020,plain,
% 2.74/2.97 (~b(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[5981, 11019, 11017, 10977])).
% 2.74/2.97 tff(11021,plain,
% 2.74/2.97 (r(z, s(s(z)))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[124, 11020])).
% 2.74/2.97 tff(11022,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(11023,plain,
% 2.74/2.97 (((~r(z, s(s(z)))) | (~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(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(11024,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[11023])).
% 2.74/2.97 tff(11025,plain,
% 2.74/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[11024, 11022])).
% 2.74/2.97 tff(11026,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(11027,plain,
% 2.74/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[11026, 11025])).
% 2.74/2.97 tff(11028,plain,
% 2.74/2.97 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[11027, 106, 11011, 11021, 10696])).
% 2.74/2.97 tff(11029,plain,
% 2.74/2.97 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[205, 11028])).
% 2.74/2.97 tff(11030,plain,
% 2.74/2.97 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8177, 10710, 1998, 10990])).
% 2.74/2.97 tff(11031,plain,
% 2.74/2.97 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10361, 11030])).
% 2.74/2.97 tff(11032,plain,
% 2.74/2.97 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8970, 11029, 10693, 11009, 11013])).
% 2.74/2.97 tff(11033,plain,
% 2.74/2.97 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[1368, 11032])).
% 2.74/2.97 tff(11034,plain,
% 2.74/2.97 (~r(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[10522, 11033, 10696, 10712])).
% 2.74/2.97 tff(11035,plain,
% 2.74/2.97 (b(z, s(s(s(z))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9192, 11034])).
% 2.74/2.97 tff(11036,plain,
% 2.74/2.97 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[9700, 11035, 10975, 10977, 11031])).
% 2.74/2.97 tff(11037,plain,
% 2.74/2.97 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[2614, 11036])).
% 2.74/2.97 tff(11038,plain,
% 2.74/2.97 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[8762, 11037, 9843, 260])).
% 2.74/2.97 tff(11039,plain,
% 2.74/2.97 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.97 inference(unit_resolution,[status(thm)],[427, 11038])).
% 2.74/2.97 tff(11040,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(11041,plain,
% 2.74/2.97 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(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)))))))),
% 2.74/2.97 inference(rewrite,[status(thm)],[])).
% 2.74/2.97 tff(11042,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.74/2.97 inference(monotonicity,[status(thm)],[11041])).
% 2.74/2.97 tff(11043,plain,
% 2.74/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.97 inference(transitivity,[status(thm)],[11042, 11040])).
% 2.74/2.97 tff(11044,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/2.97 inference(quant_inst,[status(thm)],[])).
% 2.74/2.97 tff(11045,plain,
% 2.74/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.74/2.97 inference(modus_ponens,[status(thm)],[11044, 11043])).
% 2.74/2.97 tff(11046,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11045, 171, 11039, 11029, 11019, 11017])).
% 2.74/2.98 tff(11047,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(11048,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11047, 4, 3281, 1998])).
% 2.74/2.98 tff(11049,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[3668, 11048])).
% 2.74/2.98 tff(11050,plain,
% 2.74/2.98 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9676, 11049, 10693, 3281])).
% 2.74/2.98 tff(11051,plain,
% 2.74/2.98 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9955, 11050])).
% 2.74/2.98 tff(11052,plain,
% 2.74/2.98 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11002, 2, 1998, 11051])).
% 2.74/2.98 tff(11053,plain,
% 2.74/2.98 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9958, 11052])).
% 2.74/2.98 tff(11054,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11055,plain,
% 2.74/2.98 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11056,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[11055])).
% 2.74/2.98 tff(11057,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[11056, 11054])).
% 2.74/2.98 tff(11058,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(11059,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[11058, 11057])).
% 2.74/2.98 tff(11060,plain,
% 2.74/2.98 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11059, 106, 2, 1998, 11051])).
% 2.74/2.98 tff(11061,plain,
% 2.74/2.98 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[351, 11060])).
% 2.74/2.98 tff(11062,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11063,plain,
% 2.74/2.98 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11064,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[11063])).
% 2.74/2.98 tff(11065,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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)))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[11064, 11062])).
% 2.74/2.98 tff(11066,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(11067,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(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))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[11066, 11065])).
% 2.74/2.98 tff(11068,plain,
% 2.74/2.98 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11067, 171, 11049, 83, 11061])).
% 2.74/2.98 tff(11069,plain,
% 2.74/2.98 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[225, 11068])).
% 2.74/2.98 tff(11070,plain,
% 2.74/2.98 (~r(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10398, 11069, 3281, 4])).
% 2.74/2.98 tff(11071,plain,
% 2.74/2.98 (b(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[157, 11070])).
% 2.74/2.98 tff(11072,plain,
% 2.74/2.98 (~b(s(z), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10237, 11071, 3281])).
% 2.74/2.98 tff(11073,plain,
% 2.74/2.98 (r(s(z), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[550, 11072])).
% 2.74/2.98 tff(11074,plain,
% 2.74/2.98 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8788, 11073, 1998, 2])).
% 2.74/2.98 tff(11075,plain,
% 2.74/2.98 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2642, 11074])).
% 2.74/2.98 tff(11076,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8894, 11075, 10975, 11053])).
% 2.74/2.98 tff(11077,plain,
% 2.74/2.98 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10128, 171, 11049, 4, 11061])).
% 2.74/2.98 tff(11078,plain,
% 2.74/2.98 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11077, 83])).
% 2.74/2.98 tff(11079,plain,
% 2.74/2.98 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[205, 11078])).
% 2.74/2.98 tff(11080,plain,
% 2.74/2.98 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9808, 11049, 10693, 4])).
% 2.74/2.98 tff(11081,plain,
% 2.74/2.98 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9990, 11080])).
% 2.74/2.98 tff(11082,plain,
% 2.74/2.98 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8179, 83, 10693, 11049, 11081, 11051])).
% 2.74/2.98 tff(11083,plain,
% 2.74/2.98 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[2614, 11082])).
% 2.74/2.98 tff(11084,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11085,plain,
% 2.74/2.98 (((~r(s(s(s(s(s(z))))), z)) | (~r(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(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11086,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[11085])).
% 2.74/2.98 tff(11087,plain,
% 2.74/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[11086, 11084])).
% 2.74/2.98 tff(11088,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(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(z))))))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(11089,plain,
% 2.74/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[11088, 11087])).
% 2.74/2.98 tff(11090,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11089, 106, 11083, 10696, 11079, 11076])).
% 2.74/2.98 tff(11091,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(11092,plain,
% 2.74/2.98 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11091, 2, 1998, 3281, 4])).
% 2.74/2.98 tff(11093,plain,
% 2.74/2.98 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[427, 11092])).
% 2.74/2.98 tff(11094,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10915, 106, 5609, 5567, 127, 263])).
% 2.74/2.98 tff(11095,plain,((~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)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(11096,plain,
% 2.74/2.98 (~r(z, s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11095, 11093, 10696, 11051])).
% 2.74/2.98 tff(11097,plain,
% 2.74/2.98 (b(z, s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[293, 11096])).
% 2.74/2.98 tff(11098,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11099,plain,
% 2.74/2.98 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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(z, 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(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11100,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[11099])).
% 2.74/2.98 tff(11101,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[11100, 11098])).
% 2.74/2.98 tff(11102,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(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)))),
% 2.74/2.98 inference(quant_inst,[status(thm)],[])).
% 2.74/2.98 tff(11103,plain,
% 2.74/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.98 inference(modus_ponens,[status(thm)],[11102, 11101])).
% 2.74/2.98 tff(11104,plain,
% 2.74/2.98 ((~b(s(s(z)), z)) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11103, 171, 3281, 11049, 4, 11061])).
% 2.74/2.98 tff(11105,plain,
% 2.74/2.98 (~b(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11104, 11097])).
% 2.74/2.98 tff(11106,plain,
% 2.74/2.98 (r(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[157, 11105])).
% 2.74/2.98 tff(11107,plain,
% 2.74/2.98 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10398, 11106, 3281, 4])).
% 2.74/2.98 tff(11108,plain,
% 2.74/2.98 (~b(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9563, 11093, 11053, 10696, 11061])).
% 2.74/2.98 tff(11109,plain,
% 2.74/2.98 (r(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[124, 11108])).
% 2.74/2.98 tff(11110,plain,
% 2.74/2.98 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9002, 11109, 9843, 11093])).
% 2.74/2.98 tff(11111,plain,
% 2.74/2.98 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[205, 11110])).
% 2.74/2.98 tff(11112,plain,
% 2.74/2.98 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[5760, 11111, 11049, 11053])).
% 2.74/2.98 tff(11113,plain,
% 2.74/2.98 ($false),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[225, 11112, 11107])).
% 2.74/2.98 tff(11114,plain,((~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.98 tff(11115,plain,
% 2.74/2.98 (~r(s(s(z)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11114, 4, 3281, 1998])).
% 2.74/2.98 tff(11116,plain,
% 2.74/2.98 (b(s(s(z)), s(z))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[244, 11115])).
% 2.74/2.98 tff(11117,plain,
% 2.74/2.98 (~b(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[9749, 11116, 10693, 3281, 4])).
% 2.74/2.98 tff(11118,plain,
% 2.74/2.98 (r(z, s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[124, 11117])).
% 2.74/2.98 tff(11119,plain,
% 2.74/2.98 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[8101, 11118, 10693, 4, 10696, 11116])).
% 2.74/2.98 tff(11120,plain,
% 2.74/2.98 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[427, 11119])).
% 2.74/2.98 tff(11121,plain,
% 2.74/2.98 (~r(z, s(s(s(s(z)))))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[11095, 11120, 10696, 11051])).
% 2.74/2.98 tff(11122,plain,
% 2.74/2.98 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10546, 11116, 3281, 4])).
% 2.74/2.98 tff(11123,plain,
% 2.74/2.98 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[225, 11122])).
% 2.74/2.98 tff(11124,plain,
% 2.74/2.98 (~r(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[10398, 11123, 3281, 4])).
% 2.74/2.98 tff(11125,plain,
% 2.74/2.98 (b(s(s(z)), z)),
% 2.74/2.98 inference(unit_resolution,[status(thm)],[157, 11124])).
% 2.74/2.98 tff(11126,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11127,plain,
% 2.74/2.98 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(rewrite,[status(thm)],[])).
% 2.74/2.98 tff(11128,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 2.74/2.98 inference(monotonicity,[status(thm)],[11127])).
% 2.74/2.98 tff(11129,plain,
% 2.74/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 2.74/2.98 inference(transitivity,[status(thm)],[11128, 11126])).
% 2.74/2.99 tff(11130,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11131,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11130, 11129])).
% 2.74/2.99 tff(11132,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11131, 171, 259, 1, 9835, 3686, 10693, 2527])).
% 2.74/2.99 tff(11133,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11134,plain,
% 2.74/2.99 (~b(z, s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11133, 11125, 11049, 11116])).
% 2.74/2.99 tff(11135,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[293, 11134, 11121])).
% 2.74/2.99 tff(11136,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11137,plain,
% 2.74/2.99 (~b(s(s(s(s(s(z))))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11136, 3281, 1998])).
% 2.74/2.99 tff(11138,plain,
% 2.74/2.99 (r(s(s(s(s(s(z))))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[479, 11137])).
% 2.74/2.99 tff(11139,plain,
% 2.74/2.99 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10955, 10698, 1998, 11138])).
% 2.74/2.99 tff(11140,plain,
% 2.74/2.99 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[225, 11139])).
% 2.74/2.99 tff(11141,plain,
% 2.74/2.99 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10963, 106, 10698, 11138, 1998])).
% 2.74/2.99 tff(11142,plain,
% 2.74/2.99 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[205, 11141])).
% 2.74/2.99 tff(11143,plain,
% 2.74/2.99 (~b(s(z), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8497, 171, 10693, 11142, 11140])).
% 2.74/2.99 tff(11144,plain,
% 2.74/2.99 (r(s(z), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[550, 11143])).
% 2.74/2.99 tff(11145,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9352, 11144, 11138, 10698])).
% 2.74/2.99 tff(11146,plain,
% 2.74/2.99 (b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1173, 11145])).
% 2.74/2.99 tff(11147,plain,
% 2.74/2.99 (~b(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10424, 11146, 3281])).
% 2.74/2.99 tff(11148,plain,
% 2.74/2.99 (r(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10429, 11147])).
% 2.74/2.99 tff(11149,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10579, 11148, 3281, 357])).
% 2.74/2.99 tff(11150,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10361, 11149])).
% 2.74/2.99 tff(11151,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11152,plain,
% 2.74/2.99 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(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)))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11153,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[11152])).
% 2.74/2.99 tff(11154,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[11153, 11151])).
% 2.74/2.99 tff(11155,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11156,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11155, 11154])).
% 2.74/2.99 tff(11157,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11156, 171, 1188, 376, 6462, 2852])).
% 2.74/2.99 tff(11158,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11159,plain,
% 2.74/2.99 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11158, 11150, 10975, 11146])).
% 2.74/2.99 tff(11160,plain,
% 2.74/2.99 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9990, 11159])).
% 2.74/2.99 tff(11161,plain,
% 2.74/2.99 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[5971, 11160, 10700, 10698])).
% 2.74/2.99 tff(11162,plain,
% 2.74/2.99 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[351, 11161])).
% 2.74/2.99 tff(11163,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8788, 11144, 1998, 10698])).
% 2.74/2.99 tff(11164,plain,
% 2.74/2.99 (b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2642, 11163])).
% 2.74/2.99 tff(11165,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11166,plain,
% 2.74/2.99 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), 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(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11167,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[11166])).
% 2.74/2.99 tff(11168,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[11167, 11165])).
% 2.74/2.99 tff(11169,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11170,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11169, 11168])).
% 2.74/2.99 tff(11171,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11170, 171, 2705, 6462, 2740, 2352])).
% 2.74/2.99 tff(11172,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11173,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11172, 11164, 10975, 11162])).
% 2.74/2.99 tff(11174,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(z))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10462, 11173])).
% 2.74/2.99 tff(11175,plain,
% 2.74/2.99 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[7068, 11160, 11138, 10700])).
% 2.74/2.99 tff(11176,plain,
% 2.74/2.99 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[427, 11175])).
% 2.74/2.99 tff(11177,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(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)))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11178,plain,
% 2.74/2.99 (((~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(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(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11179,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[11178])).
% 2.74/2.99 tff(11180,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[11179, 11177])).
% 2.74/2.99 tff(11181,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(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))))))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11182,plain,
% 2.74/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11181, 11180])).
% 2.74/2.99 tff(11183,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11182, 171, 11164, 11176, 11142, 11140])).
% 2.74/2.99 tff(11184,plain,
% 2.74/2.99 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2614, 11183])).
% 2.74/2.99 tff(11185,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11186,plain,
% 2.74/2.99 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~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(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11187,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[11186])).
% 2.74/2.99 tff(11188,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[11187, 11185])).
% 2.74/2.99 tff(11189,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11190,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11189, 11188])).
% 2.74/2.99 tff(11191,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11190, 106, 10698, 11184, 1998, 11174])).
% 2.74/2.99 tff(11192,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11193,plain,
% 2.74/2.99 (~b(s(s(s(s(z)))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11192, 3281, 1998])).
% 2.74/2.99 tff(11194,plain,
% 2.74/2.99 (r(s(s(s(s(z)))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9955, 11193])).
% 2.74/2.99 tff(11195,plain,
% 2.74/2.99 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2312, 11194, 1998, 11138])).
% 2.74/2.99 tff(11196,plain,
% 2.74/2.99 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[3668, 11195])).
% 2.74/2.99 tff(11197,plain,
% 2.74/2.99 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9104, 11196, 10693, 1998, 11138])).
% 2.74/2.99 tff(11198,plain,
% 2.74/2.99 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[427, 11197])).
% 2.74/2.99 tff(11199,plain,
% 2.74/2.99 (~r(s(z), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[7054, 11198, 11138, 11194])).
% 2.74/2.99 tff(11200,plain,
% 2.74/2.99 (b(s(z), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[550, 11199])).
% 2.74/2.99 tff(11201,plain,
% 2.74/2.99 (~b(s(z), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10353, 10319, 10321, 259, 323, 3686])).
% 2.74/2.99 tff(11202,plain,
% 2.74/2.99 (r(s(z), s(s(s(s(z)))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9990, 11201])).
% 2.74/2.99 tff(11203,plain,
% 2.74/2.99 (~r(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8249, 11202, 502, 3686])).
% 2.74/2.99 tff(11204,plain,
% 2.74/2.99 (b(s(s(s(z))), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[1173, 11203])).
% 2.74/2.99 tff(11205,plain,
% 2.74/2.99 (~b(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10424, 11204, 3281])).
% 2.74/2.99 tff(11206,plain,
% 2.74/2.99 (r(s(s(s(z))), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10429, 11205])).
% 2.74/2.99 tff(11207,plain,
% 2.74/2.99 (~b(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2707, 11204, 259, 323])).
% 2.74/2.99 tff(11208,plain,
% 2.74/2.99 (r(s(s(s(z))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[2642, 11207])).
% 2.74/2.99 tff(11209,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[8282, 106, 10321, 10319, 11208, 11206])).
% 2.74/2.99 tff(11210,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11211,plain,
% 2.74/2.99 (~b(s(s(z)), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11210, 11200, 3281, 11138, 11196])).
% 2.74/2.99 tff(11212,plain,
% 2.74/2.99 (r(s(s(z)), s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[244, 11211])).
% 2.74/2.99 tff(11213,plain,
% 2.74/2.99 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11002, 11212, 1998, 11194])).
% 2.74/2.99 tff(11214,plain,
% 2.74/2.99 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[9958, 11213])).
% 2.74/2.99 tff(11215,plain,
% 2.74/2.99 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10955, 11212, 1998, 11138])).
% 2.74/2.99 tff(11216,plain,
% 2.74/2.99 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[225, 11215])).
% 2.74/2.99 tff(11217,plain,
% 2.74/2.99 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[5760, 11216, 11196, 11214])).
% 2.74/2.99 tff(11218,plain,
% 2.74/2.99 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[205, 11217])).
% 2.74/2.99 tff(11219,plain,
% 2.74/2.99 ($false),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[10963, 106, 11212, 11138, 1998, 11218])).
% 2.74/2.99 tff(11220,plain,((~b(z, s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/2.99 tff(11221,plain,
% 2.74/2.99 (~b(z, s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11220, 1998])).
% 2.74/2.99 tff(11222,plain,
% 2.74/2.99 (r(z, s(z))),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[93, 11221])).
% 2.74/2.99 tff(11223,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11224,plain,
% 2.74/2.99 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11225,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.74/2.99 inference(monotonicity,[status(thm)],[11224])).
% 2.74/2.99 tff(11226,plain,
% 2.74/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 2.74/2.99 inference(transitivity,[status(thm)],[11225, 11223])).
% 2.74/2.99 tff(11227,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.74/2.99 inference(quant_inst,[status(thm)],[])).
% 2.74/2.99 tff(11228,plain,
% 2.74/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))),
% 2.74/2.99 inference(modus_ponens,[status(thm)],[11227, 11226])).
% 2.74/2.99 tff(11229,plain,
% 2.74/2.99 (~r(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[11228, 106, 11222, 2, 1998])).
% 2.74/2.99 tff(11230,plain,
% 2.74/2.99 (b(s(s(z)), z)),
% 2.74/2.99 inference(unit_resolution,[status(thm)],[157, 11229])).
% 2.74/2.99 tff(11231,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11232,plain,
% 2.74/2.99 (((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/2.99 inference(rewrite,[status(thm)],[])).
% 2.74/2.99 tff(11233,plain,
% 2.74/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11232])).
% 2.74/3.00 tff(11234,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11233, 11231])).
% 2.74/3.00 tff(11235,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11236,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11235, 11234])).
% 2.74/3.00 tff(11237,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11236, 171, 1188, 10693, 1384, 4])).
% 2.74/3.00 tff(11238,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(11239,plain,
% 2.74/3.00 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11238, 1188, 4])).
% 2.74/3.00 tff(11240,plain,
% 2.74/3.00 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1368, 11239])).
% 2.74/3.00 tff(11241,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11242,plain,
% 2.74/3.00 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11243,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11242])).
% 2.74/3.00 tff(11244,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11243, 11241])).
% 2.74/3.00 tff(11245,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11246,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11245, 11244])).
% 2.74/3.00 tff(11247,plain,
% 2.74/3.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11246, 106, 260, 11240, 501])).
% 2.74/3.00 tff(11248,plain,
% 2.74/3.00 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[9958, 11247])).
% 2.74/3.00 tff(11249,plain,
% 2.74/3.00 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[4732, 171, 1188, 10693, 4])).
% 2.74/3.00 tff(11250,plain,
% 2.74/3.00 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[2614, 11249])).
% 2.74/3.00 tff(11251,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[8553, 106, 260, 2604, 1357, 6477])).
% 2.74/3.00 tff(11252,plain,((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(11253,plain,
% 2.74/3.00 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11252, 11250, 260, 11240])).
% 2.74/3.00 tff(11254,plain,
% 2.74/3.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[6475, 11253])).
% 2.74/3.00 tff(11255,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11256,plain,
% 2.74/3.00 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z)))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11257,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11256])).
% 2.74/3.00 tff(11258,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11257, 11255])).
% 2.74/3.00 tff(11259,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(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(z))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11260,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11259, 11258])).
% 2.74/3.00 tff(11261,plain,
% 2.74/3.00 (~r(s(s(z)), s(s(s(z))))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11260, 106, 11250, 11240, 501])).
% 2.74/3.00 tff(11262,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11263,plain,
% 2.74/3.00 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11264,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11263])).
% 2.74/3.00 tff(11265,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11264, 11262])).
% 2.74/3.00 tff(11266,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11267,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11266, 11265])).
% 2.74/3.00 tff(11268,plain,
% 2.74/3.00 (~r(s(s(s(z))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11267, 106, 11250, 11240, 501])).
% 2.74/3.00 tff(11269,plain,
% 2.74/3.00 (b(s(s(s(z))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[2642, 11268])).
% 2.74/3.00 tff(11270,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[8894, 11269, 11261, 11254, 11248])).
% 2.74/3.00 tff(11271,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(11272,plain,
% 2.74/3.00 (~b(s(s(s(z))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11271, 501, 260, 4])).
% 2.74/3.00 tff(11273,plain,
% 2.74/3.00 (r(s(s(s(z))), s(z))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[1173, 11272])).
% 2.74/3.00 tff(11274,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11275,plain,
% 2.74/3.00 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11276,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11275])).
% 2.74/3.00 tff(11277,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11276, 11274])).
% 2.74/3.00 tff(11278,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11279,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11278, 11277])).
% 2.74/3.00 tff(11280,plain,
% 2.74/3.00 (~r(s(s(s(z))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11279, 106, 554, 96, 747])).
% 2.74/3.00 tff(11281,plain,
% 2.74/3.00 (b(s(s(s(z))), z)),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[10429, 11280])).
% 2.74/3.00 tff(11282,plain,
% 2.74/3.00 (b(s(s(s(z))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[2642, 9343])).
% 2.74/3.00 tff(11283,plain,
% 2.74/3.00 (~r(z, s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[624, 554, 96, 501])).
% 2.74/3.00 tff(11284,plain,
% 2.74/3.00 (b(z, s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[124, 11283])).
% 2.74/3.00 tff(11285,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11286,plain,
% 2.74/3.00 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11287,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11286])).
% 2.74/3.00 tff(11288,plain,
% 2.74/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11287, 11285])).
% 2.74/3.00 tff(11289,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11290,plain,
% 2.74/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 2.74/3.00 inference(modus_ponens,[status(thm)],[11289, 11288])).
% 2.74/3.00 tff(11291,plain,
% 2.74/3.00 ($false),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11290, 171, 11284, 1, 11282, 11281])).
% 2.74/3.00 tff(11292,plain,((~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.00 tff(11293,plain,
% 2.74/3.00 (~r(s(z), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11292, 11273, 2, 1, 96, 501])).
% 2.74/3.00 tff(11294,plain,
% 2.74/3.00 (b(s(z), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[550, 11293])).
% 2.74/3.00 tff(11295,plain,
% 2.74/3.00 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[11246, 106, 260, 1357, 501])).
% 2.74/3.00 tff(11296,plain,
% 2.74/3.00 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.00 inference(unit_resolution,[status(thm)],[9958, 11295])).
% 2.74/3.00 tff(11297,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11298,plain,
% 2.74/3.00 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), 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(s(s(s(z))))), s(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))))))))),
% 2.74/3.00 inference(rewrite,[status(thm)],[])).
% 2.74/3.00 tff(11299,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.74/3.00 inference(monotonicity,[status(thm)],[11298])).
% 2.74/3.00 tff(11300,plain,
% 2.74/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.74/3.00 inference(transitivity,[status(thm)],[11299, 11297])).
% 2.74/3.00 tff(11301,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.74/3.00 inference(quant_inst,[status(thm)],[])).
% 2.74/3.00 tff(11302,plain,
% 2.74/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11301, 11300])).
% 2.74/3.01 tff(11303,plain,
% 2.74/3.01 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11302, 106, 260, 1357, 501])).
% 2.74/3.01 tff(11304,plain,
% 2.74/3.01 (b(s(s(z)), s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[351, 11303])).
% 2.74/3.01 tff(11305,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11306,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(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11307,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[11306])).
% 2.74/3.01 tff(11308,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[11307, 11305])).
% 2.74/3.01 tff(11309,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(11310,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11309, 11308])).
% 2.74/3.01 tff(11311,plain,
% 2.74/3.01 (~b(s(z), s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11310, 171, 323, 11296, 11304])).
% 2.74/3.01 tff(11312,plain,
% 2.74/3.01 (r(s(z), s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9990, 11311])).
% 2.74/3.01 tff(11313,plain,
% 2.74/3.01 (~r(z, s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10152, 11312, 96, 260])).
% 2.74/3.01 tff(11314,plain,
% 2.74/3.01 (b(z, s(s(s(s(z)))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[293, 11313])).
% 2.74/3.01 tff(11315,plain,
% 2.74/3.01 (~b(s(s(s(s(z)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2535, 11314, 1, 11296])).
% 2.74/3.01 tff(11316,plain,
% 2.74/3.01 (r(s(s(s(s(z)))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[274, 11315])).
% 2.74/3.01 tff(11317,plain,
% 2.74/3.01 (~b(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9082, 171, 323, 11296, 11304])).
% 2.74/3.01 tff(11318,plain,
% 2.74/3.01 (r(s(s(s(s(z)))), s(z))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9955, 11317])).
% 2.74/3.01 tff(11319,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[4291, 106, 96, 11312, 11318, 11316])).
% 2.74/3.01 tff(11320,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(11321,plain,
% 2.74/3.01 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11320, 11294, 1, 260, 96, 501])).
% 2.74/3.01 tff(11322,plain,
% 2.74/3.01 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1368, 11321])).
% 2.74/3.01 tff(11323,plain,
% 2.74/3.01 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11324,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[11323])).
% 2.74/3.01 tff(11325,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)))),
% 2.74/3.01 inference(transitivity,[status(thm)],[11324, 9863])).
% 2.74/3.01 tff(11326,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(11327,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11326, 11325])).
% 2.74/3.01 tff(11328,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11327, 171, 323, 161, 1, 9835])).
% 2.74/3.01 tff(11329,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(11330,plain,
% 2.74/3.01 (~b(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11329, 11294, 1])).
% 2.74/3.01 tff(11331,plain,
% 2.74/3.01 (r(z, s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[124, 11330])).
% 2.74/3.01 tff(11332,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11333,plain,
% 2.74/3.01 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11334,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[11333])).
% 2.74/3.01 tff(11335,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[11334, 11332])).
% 2.74/3.01 tff(11336,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(11337,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11336, 11335])).
% 2.74/3.01 tff(11338,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11337, 106, 96, 2, 600, 1998])).
% 2.74/3.01 tff(11339,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(11340,plain,
% 2.74/3.01 (~r(s(z), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11339, 11331, 2, 96])).
% 2.74/3.01 tff(11341,plain,
% 2.74/3.01 (b(s(z), s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[1996, 11340])).
% 2.74/3.01 tff(11342,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11343,plain,
% 2.74/3.01 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11344,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/3.01 inference(monotonicity,[status(thm)],[11343])).
% 2.74/3.01 tff(11345,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.01 inference(transitivity,[status(thm)],[11344, 11342])).
% 2.74/3.01 tff(11346,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(11347,plain,
% 2.74/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11346, 11345])).
% 2.74/3.01 tff(11348,plain,
% 2.74/3.01 ($false),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11347, 171, 1, 9835, 2705, 1976, 1384, 4])).
% 2.74/3.01 tff(11349,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.01 tff(11350,plain,
% 2.74/3.01 (~b(s(s(s(z))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11349, 11341, 1, 11322, 4])).
% 2.74/3.01 tff(11351,plain,
% 2.74/3.01 (r(s(s(s(z))), s(s(z)))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[2642, 11350])).
% 2.74/3.01 tff(11352,plain,
% 2.74/3.01 (~r(z, s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10273, 106, 2, 11331, 11351])).
% 2.74/3.01 tff(11353,plain,
% 2.74/3.01 (b(z, s(s(s(z))))),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[9192, 11352])).
% 2.74/3.01 tff(11354,plain,
% 2.74/3.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11355,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.74/3.01 inference(quant_inst,[status(thm)],[])).
% 2.74/3.01 tff(11356,plain,
% 2.74/3.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 2.74/3.01 inference(modus_ponens,[status(thm)],[11355, 11354])).
% 2.74/3.01 tff(11357,plain,
% 2.74/3.01 (~r(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[11356, 106, 2, 11331, 11351])).
% 2.74/3.01 tff(11358,plain,
% 2.74/3.01 (b(s(s(s(z))), z)),
% 2.74/3.01 inference(unit_resolution,[status(thm)],[10429, 11357])).
% 2.74/3.01 tff(11359,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11360,plain,
% 2.74/3.01 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/3.01 inference(rewrite,[status(thm)],[])).
% 2.74/3.01 tff(11361,plain,
% 2.74/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[11360])).
% 2.74/3.02 tff(11362,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[11361, 11359])).
% 2.74/3.02 tff(11363,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(11364,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[11363, 11362])).
% 2.74/3.02 tff(11365,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11364, 171, 11341, 11322, 4, 11358, 11353])).
% 2.74/3.02 tff(11366,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(11367,plain,
% 2.74/3.02 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11366, 260, 2, 1, 96, 4])).
% 2.74/3.02 tff(11368,plain,
% 2.74/3.02 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[205, 11367])).
% 2.74/3.02 tff(11369,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11370,plain,
% 2.74/3.02 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11371,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[11370])).
% 2.74/3.02 tff(11372,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[11371, 11369])).
% 2.74/3.02 tff(11373,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(11374,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[11373, 11372])).
% 2.74/3.02 tff(11375,plain,
% 2.74/3.02 ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11374, 171, 1, 9835, 10693, 4])).
% 2.74/3.02 tff(11376,plain,
% 2.74/3.02 (~b(s(z), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11375, 11368])).
% 2.74/3.02 tff(11377,plain,
% 2.74/3.02 (r(s(z), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[550, 11376])).
% 2.74/3.02 tff(11378,plain,
% 2.74/3.02 (~b(z, s(s(s(s(s(z))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[8800, 11368, 10693, 1, 4])).
% 2.74/3.02 tff(11379,plain,
% 2.74/3.02 (r(z, s(s(s(s(s(z))))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[498, 11378])).
% 2.74/3.02 tff(11380,plain,
% 2.74/3.02 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[8790, 11379, 10693, 1, 4, 2, 260, 11377])).
% 2.74/3.02 tff(11381,plain,
% 2.74/3.02 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[427, 11380])).
% 2.74/3.02 tff(11382,plain,
% 2.74/3.02 (~b(s(s(s(s(z)))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[8053, 11381, 10693, 4])).
% 2.74/3.02 tff(11383,plain,
% 2.74/3.02 (r(s(s(s(s(z)))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[9955, 11382])).
% 2.74/3.02 tff(11384,plain,
% 2.74/3.02 (~r(z, s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[8816, 106, 11377, 96, 2])).
% 2.74/3.02 tff(11385,plain,
% 2.74/3.02 (b(z, s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[124, 11384])).
% 2.74/3.02 tff(11386,plain,
% 2.74/3.02 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[10886, 106, 554, 2, 263])).
% 2.74/3.02 tff(11387,plain,
% 2.74/3.02 (b(s(s(s(s(z)))), s(s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[374, 11386, 369])).
% 2.74/3.02 tff(11388,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11389,plain,
% 2.74/3.02 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11390,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[11389])).
% 2.74/3.02 tff(11391,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[11390, 11388])).
% 2.74/3.02 tff(11392,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(11393,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[11392, 11391])).
% 2.74/3.02 tff(11394,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11393, 106, 554, 263, 747, 2828])).
% 2.74/3.02 tff(11395,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(11396,plain,
% 2.74/3.02 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11395, 263, 554, 747])).
% 2.74/3.02 tff(11397,plain,
% 2.74/3.02 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1102, 25, 1187, 11396])).
% 2.74/3.02 tff(11398,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11399,plain,
% 2.74/3.02 (((~b(z, 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(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11400,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.74/3.02 inference(monotonicity,[status(thm)],[11399])).
% 2.74/3.02 tff(11401,plain,
% 2.74/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(transitivity,[status(thm)],[11400, 11398])).
% 2.74/3.02 tff(11402,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(11403,plain,
% 2.74/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[11402, 11401])).
% 2.74/3.02 tff(11404,plain,
% 2.74/3.02 ($false),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11403, 171, 161, 1, 9344, 11397, 11387])).
% 2.74/3.02 tff(11405,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(s(s(z)))) = s(s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.74/3.02 tff(11406,plain,
% 2.74/3.02 ((~r(s(s(s(s(z)))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11405, 355])).
% 2.74/3.02 tff(11407,plain,
% 2.74/3.02 (~r(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11406, 11385, 11377, 11383, 2, 1])).
% 2.74/3.02 tff(11408,plain,
% 2.74/3.02 (b(s(s(s(z))), s(z))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1173, 11407])).
% 2.74/3.02 tff(11409,plain,
% 2.74/3.02 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11238, 11408, 4])).
% 2.74/3.02 tff(11410,plain,
% 2.74/3.02 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[1368, 11409])).
% 2.74/3.02 tff(11411,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11412,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 2.74/3.02 inference(quant_inst,[status(thm)],[])).
% 2.74/3.02 tff(11413,plain,
% 2.74/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 2.74/3.02 inference(modus_ponens,[status(thm)],[11412, 11411])).
% 2.74/3.02 tff(11414,plain,
% 2.74/3.02 (~r(z, s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[11413, 106, 260, 11410, 11379])).
% 2.74/3.02 tff(11415,plain,
% 2.74/3.02 (b(z, s(s(s(s(z)))))),
% 2.74/3.02 inference(unit_resolution,[status(thm)],[293, 11414])).
% 2.74/3.02 tff(11416,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11417,plain,
% 2.74/3.02 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.74/3.02 inference(rewrite,[status(thm)],[])).
% 2.74/3.02 tff(11418,plain,
% 2.74/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[11417])).
% 2.86/3.02 tff(11419,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(transitivity,[status(thm)],[11418, 11416])).
% 2.86/3.02 tff(11420,plain,
% 2.86/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)))),
% 2.86/3.02 inference(quant_inst,[status(thm)],[])).
% 2.86/3.02 tff(11421,plain,
% 2.86/3.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.86/3.02 inference(modus_ponens,[status(thm)],[11420, 11419])).
% 2.86/3.02 tff(11422,plain,
% 2.86/3.02 (~r(s(s(s(s(z)))), z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[11421, 106, 260, 11410, 11379])).
% 2.86/3.02 tff(11423,plain,
% 2.86/3.02 (b(s(s(s(s(z)))), z)),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[274, 11422])).
% 2.86/3.02 tff(11424,plain,
% 2.86/3.02 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[2535, 11423, 1, 11415])).
% 2.86/3.02 tff(11425,plain,
% 2.86/3.02 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[9958, 11424])).
% 2.86/3.02 tff(11426,plain,
% 2.86/3.02 (~r(s(z), s(s(s(s(z)))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[6011, 11425, 2, 11383])).
% 2.86/3.02 tff(11427,plain,
% 2.86/3.02 (b(s(z), s(s(s(s(z)))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[9990, 11426])).
% 2.86/3.02 tff(11428,plain,
% 2.86/3.02 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[11252, 1357, 260, 2604])).
% 2.86/3.02 tff(11429,plain,
% 2.86/3.02 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[6475, 11428])).
% 2.86/3.02 tff(11430,plain,
% 2.86/3.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[11158, 11429, 376, 1188])).
% 2.86/3.02 tff(11431,plain,
% 2.86/3.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.02 inference(unit_resolution,[status(thm)],[10361, 11430])).
% 2.86/3.02 tff(11432,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(11433,plain,
% 2.86/3.02 (((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), 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(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.02 inference(rewrite,[status(thm)],[])).
% 2.86/3.02 tff(11434,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.86/3.02 inference(monotonicity,[status(thm)],[11433])).
% 2.86/3.02 tff(11435,plain,
% 2.86/3.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11434, 11432])).
% 2.86/3.03 tff(11436,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11437,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11436, 11435])).
% 2.86/3.03 tff(11438,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11437, 106, 260, 2604, 1357, 11431])).
% 2.86/3.03 tff(11439,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11440,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11439, 11427, 260, 11410, 11408])).
% 2.86/3.03 tff(11441,plain,
% 2.86/3.03 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2614, 11440])).
% 2.86/3.03 tff(11442,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5940, 106, 554, 2, 569])).
% 2.86/3.03 tff(11443,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[321, 11442, 314])).
% 2.86/3.03 tff(11444,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11445,plain,
% 2.86/3.03 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11446,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[11445])).
% 2.86/3.03 tff(11447,plain,
% 2.86/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11446, 11444])).
% 2.86/3.03 tff(11448,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11449,plain,
% 2.86/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11448, 11447])).
% 2.86/3.03 tff(11450,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11449, 106, 2, 1199, 569, 2828])).
% 2.86/3.03 tff(11451,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11452,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11451, 569, 1199, 2])).
% 2.86/3.03 tff(11453,plain,
% 2.86/3.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2842, 11452, 2839])).
% 2.86/3.03 tff(11454,plain,
% 2.86/3.03 (~r(s(z), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[5989, 106, 554, 2, 569])).
% 2.86/3.03 tff(11455,plain,
% 2.86/3.03 (b(s(z), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[454, 11454, 447])).
% 2.86/3.03 tff(11456,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11457,plain,
% 2.86/3.03 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11458,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[11457])).
% 2.86/3.03 tff(11459,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11458, 11456])).
% 2.86/3.03 tff(11460,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11461,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11460, 11459])).
% 2.86/3.03 tff(11462,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11461, 171, 3133, 1188, 11455, 11453, 11443])).
% 2.86/3.03 tff(11463,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (s(z) = s(s(s(s(z))))) | (s(s(s(s(z)))) = s(z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (s(s(s(z))) = s(s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11464,plain,
% 2.86/3.03 ((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11463, 9835, 254, 255, 2264])).
% 2.86/3.03 tff(11465,plain,
% 2.86/3.03 (~r(s(s(s(z))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11464, 11425, 2, 11377, 11408])).
% 2.86/3.03 tff(11466,plain,
% 2.86/3.03 (b(s(s(s(z))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2642, 11465])).
% 2.86/3.03 tff(11467,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(s(s(s(z))))), s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11468,plain,
% 2.86/3.03 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(s(s(s(z))))), s(z))))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11469,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(s(s(s(z))))), s(z)))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[11468])).
% 2.86/3.03 tff(11470,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), 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(s(s(s(z))))), s(z))))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11469, 11467])).
% 2.86/3.03 tff(11471,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(z)))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11472,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11471, 11470])).
% 2.86/3.03 tff(11473,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11472, 171, 1, 9835, 11466, 11441, 4, 11368])).
% 2.86/3.03 tff(11474,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11475,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11474, 2, 4, 1, 96])).
% 2.86/3.03 tff(11476,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[3668, 11475])).
% 2.86/3.03 tff(11477,plain,
% 2.86/3.03 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8704, 11476, 10693, 4])).
% 2.86/3.03 tff(11478,plain,
% 2.86/3.03 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9955, 11477])).
% 2.86/3.03 tff(11479,plain,
% 2.86/3.03 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9808, 11476, 10693, 4])).
% 2.86/3.03 tff(11480,plain,
% 2.86/3.03 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9990, 11479])).
% 2.86/3.03 tff(11481,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[6011, 11480, 2, 11478])).
% 2.86/3.03 tff(11482,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9958, 11481])).
% 2.86/3.03 tff(11483,plain,
% 2.86/3.03 (~r(s(s(s(s(z)))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[4291, 106, 96, 11480, 11478])).
% 2.86/3.03 tff(11484,plain,
% 2.86/3.03 (b(s(s(s(s(z)))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[274, 11483])).
% 2.86/3.03 tff(11485,plain,
% 2.86/3.03 (~r(z, s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[4299, 106, 96, 11480, 11478])).
% 2.86/3.03 tff(11486,plain,
% 2.86/3.03 (b(z, s(s(s(s(z)))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[293, 11485])).
% 2.86/3.03 tff(11487,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2535, 11486, 11484, 1, 11482])).
% 2.86/3.03 tff(11488,plain,((~r(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11489,plain,
% 2.86/3.03 (~r(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11488, 4, 96, 1])).
% 2.86/3.03 tff(11490,plain,
% 2.86/3.03 (b(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[244, 11489])).
% 2.86/3.03 tff(11491,plain,
% 2.86/3.03 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8650, 171, 11490, 10693, 4])).
% 2.86/3.03 tff(11492,plain,
% 2.86/3.03 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[205, 11491])).
% 2.86/3.03 tff(11493,plain,
% 2.86/3.03 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8081, 171, 11490, 10693, 4])).
% 2.86/3.03 tff(11494,plain,
% 2.86/3.03 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[225, 11493])).
% 2.86/3.03 tff(11495,plain,
% 2.86/3.03 (~b(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9982, 11490, 1])).
% 2.86/3.03 tff(11496,plain,
% 2.86/3.03 (r(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[124, 11495])).
% 2.86/3.03 tff(11497,plain,
% 2.86/3.03 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8680, 106, 11496, 11494, 11492])).
% 2.86/3.03 tff(11498,plain,
% 2.86/3.03 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[498, 11497])).
% 2.86/3.03 tff(11499,plain,
% 2.86/3.03 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8099, 106, 11496, 11494, 11492])).
% 2.86/3.03 tff(11500,plain,
% 2.86/3.03 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[145, 11499])).
% 2.86/3.03 tff(11501,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11502,plain,
% 2.86/3.03 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11503,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[11502])).
% 2.86/3.03 tff(11504,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11503, 11501])).
% 2.86/3.03 tff(11505,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11506,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11505, 11504])).
% 2.86/3.03 tff(11507,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11506, 171, 9835, 4, 11500, 11498])).
% 2.86/3.03 tff(11508,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11509,plain,
% 2.86/3.03 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11508, 1, 96])).
% 2.86/3.03 tff(11510,plain,
% 2.86/3.03 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[479, 11509])).
% 2.86/3.03 tff(11511,plain,
% 2.86/3.03 (~b(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9932, 554, 96, 11510])).
% 2.86/3.03 tff(11512,plain,
% 2.86/3.03 (r(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[244, 11511])).
% 2.86/3.03 tff(11513,plain,
% 2.86/3.03 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[10894, 11512, 11510, 554])).
% 2.86/3.03 tff(11514,plain,
% 2.86/3.03 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[225, 11513])).
% 2.86/3.03 tff(11515,plain,
% 2.86/3.03 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9892, 106, 554, 96, 11510])).
% 2.86/3.03 tff(11516,plain,
% 2.86/3.03 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[145, 11515])).
% 2.86/3.03 tff(11517,plain,
% 2.86/3.03 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[562, 106, 554, 96, 11510])).
% 2.86/3.03 tff(11518,plain,
% 2.86/3.03 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[498, 11517])).
% 2.86/3.03 tff(11519,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[6961, 11518, 11516, 11514, 1])).
% 2.86/3.03 tff(11520,plain,((~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11521,plain,
% 2.86/3.03 (~r(s(z), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11520, 11230, 11222])).
% 2.86/3.03 tff(11522,plain,
% 2.86/3.03 (~r(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11339, 2, 1998, 11222])).
% 2.86/3.03 tff(11523,plain,
% 2.86/3.03 (b(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[124, 11522])).
% 2.86/3.03 tff(11524,plain,
% 2.86/3.03 (~b(s(z), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11329, 11230, 11523])).
% 2.86/3.03 tff(11525,plain,
% 2.86/3.03 ($false),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[550, 11524, 11521])).
% 2.86/3.03 tff(11526,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.03 tff(11527,plain,
% 2.86/3.03 (~r(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11526, 1998])).
% 2.86/3.03 tff(11528,plain,
% 2.86/3.03 (b(s(s(z)), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[244, 11527])).
% 2.86/3.03 tff(11529,plain,
% 2.86/3.03 (~b(s(s(z)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[11520, 554, 96])).
% 2.86/3.03 tff(11530,plain,
% 2.86/3.03 (r(s(s(z)), z)),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[157, 11529])).
% 2.86/3.03 tff(11531,plain,
% 2.86/3.03 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[9932, 554, 96, 259])).
% 2.86/3.03 tff(11532,plain,
% 2.86/3.03 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[479, 11531])).
% 2.86/3.03 tff(11533,plain,
% 2.86/3.03 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[8081, 171, 259, 10693, 11532])).
% 2.86/3.03 tff(11534,plain,
% 2.86/3.03 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[225, 11533])).
% 2.86/3.03 tff(11535,plain,
% 2.86/3.03 (~r(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[2549, 11530, 96, 554])).
% 2.86/3.03 tff(11536,plain,
% 2.86/3.03 (b(z, s(s(z)))),
% 2.86/3.03 inference(unit_resolution,[status(thm)],[124, 11535])).
% 2.86/3.03 tff(11537,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11538,plain,
% 2.86/3.03 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(rewrite,[status(thm)],[])).
% 2.86/3.03 tff(11539,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.86/3.03 inference(monotonicity,[status(thm)],[11538])).
% 2.86/3.03 tff(11540,plain,
% 2.86/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.03 inference(transitivity,[status(thm)],[11539, 11537])).
% 2.86/3.03 tff(11541,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.03 inference(quant_inst,[status(thm)],[])).
% 2.86/3.03 tff(11542,plain,
% 2.86/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.03 inference(modus_ponens,[status(thm)],[11541, 11540])).
% 2.86/3.04 tff(11543,plain,
% 2.86/3.04 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11542, 171, 259, 11536, 9835, 10693, 11532])).
% 2.86/3.04 tff(11544,plain,
% 2.86/3.04 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[145, 11543])).
% 2.86/3.04 tff(11545,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[959, 11544, 11534, 96, 11530])).
% 2.86/3.04 tff(11546,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11547,plain,
% 2.86/3.04 (~r(s(z), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11546, 11222, 11528])).
% 2.86/3.04 tff(11548,plain,
% 2.86/3.04 (b(s(z), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[550, 11547])).
% 2.86/3.04 tff(11549,plain,
% 2.86/3.04 (~b(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8383, 3133, 159, 1275])).
% 2.86/3.04 tff(11550,plain,
% 2.86/3.04 (r(z, s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[93, 11549])).
% 2.86/3.04 tff(11551,plain,
% 2.86/3.04 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2499, 11550, 3, 502])).
% 2.86/3.04 tff(11552,plain,
% 2.86/3.04 ((z = s(s(s(s(s(z)))))) | b(z, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[496, 25, 11551])).
% 2.86/3.04 tff(11553,plain,
% 2.86/3.04 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11552, 6021])).
% 2.86/3.04 tff(11554,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11555,plain,
% 2.86/3.04 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11556,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[11555])).
% 2.86/3.04 tff(11557,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.04 inference(transitivity,[status(thm)],[11556, 11554])).
% 2.86/3.04 tff(11558,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(11559,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[11558, 11557])).
% 2.86/3.04 tff(11560,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11559, 171, 3133, 1275, 159, 11553])).
% 2.86/3.04 tff(11561,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11562,plain,
% 2.86/3.04 ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11561, 9835])).
% 2.86/3.04 tff(11563,plain,
% 2.86/3.04 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11562, 3, 10693, 502])).
% 2.86/3.04 tff(11564,plain,
% 2.86/3.04 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[145, 11563])).
% 2.86/3.04 tff(11565,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11566,plain,
% 2.86/3.04 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11567,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[11566])).
% 2.86/3.04 tff(11568,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[11567, 11565])).
% 2.86/3.04 tff(11569,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(11570,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[11569, 11568])).
% 2.86/3.04 tff(11571,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11570, 106, 96, 502, 3, 11564])).
% 2.86/3.04 tff(11572,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11573,plain,
% 2.86/3.04 (~r(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11572, 502, 11222])).
% 2.86/3.04 tff(11574,plain,
% 2.86/3.04 (b(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9990, 11573])).
% 2.86/3.04 tff(11575,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6253, 11574, 11528, 11548])).
% 2.86/3.04 tff(11576,plain,
% 2.86/3.04 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9958, 11575])).
% 2.86/3.04 tff(11577,plain,
% 2.86/3.04 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[445, 11532, 259, 357])).
% 2.86/3.04 tff(11578,plain,
% 2.86/3.04 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9990, 11577])).
% 2.86/3.04 tff(11579,plain,
% 2.86/3.04 (~r(z, s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[10152, 11578, 96, 260])).
% 2.86/3.04 tff(11580,plain,
% 2.86/3.04 (b(z, s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[293, 11579])).
% 2.86/3.04 tff(11581,plain,
% 2.86/3.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[10070, 11578, 554, 260])).
% 2.86/3.04 tff(11582,plain,
% 2.86/3.04 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[351, 11581])).
% 2.86/3.04 tff(11583,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[5981, 11582, 11536, 11580])).
% 2.86/3.04 tff(11584,plain,
% 2.86/3.04 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9958, 11583])).
% 2.86/3.04 tff(11585,plain,
% 2.86/3.04 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[587, 11584, 259, 554, 260, 357])).
% 2.86/3.04 tff(11586,plain,
% 2.86/3.04 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[205, 11585])).
% 2.86/3.04 tff(11587,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8650, 171, 259, 10693, 11532, 11586])).
% 2.86/3.04 tff(11588,plain,((~r(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11589,plain,
% 2.86/3.04 (~r(s(z), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11588, 357, 260, 259, 96])).
% 2.86/3.04 tff(11590,plain,
% 2.86/3.04 (b(s(z), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[550, 11589])).
% 2.86/3.04 tff(11591,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[365, 11590, 259, 357])).
% 2.86/3.04 tff(11592,plain,
% 2.86/3.04 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9958, 11591])).
% 2.86/3.04 tff(11593,plain,
% 2.86/3.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[6512, 11590, 259, 357])).
% 2.86/3.04 tff(11594,plain,
% 2.86/3.04 (r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[351, 11593])).
% 2.86/3.04 tff(11595,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11596,plain,
% 2.86/3.04 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11597,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[11596])).
% 2.86/3.04 tff(11598,plain,
% 2.86/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[11597, 11595])).
% 2.86/3.04 tff(11599,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(11600,plain,
% 2.86/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[11599, 11598])).
% 2.86/3.04 tff(11601,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11600, 171, 323, 259, 161, 9835])).
% 2.86/3.04 tff(11602,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11603,plain,
% 2.86/3.04 (~b(z, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11602, 11590, 259])).
% 2.86/3.04 tff(11604,plain,
% 2.86/3.04 (r(z, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[124, 11603])).
% 2.86/3.04 tff(11605,plain,
% 2.86/3.04 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[10009, 11604, 357, 11592, 11594])).
% 2.86/3.04 tff(11606,plain,
% 2.86/3.04 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9990, 11605])).
% 2.86/3.04 tff(11607,plain,
% 2.86/3.04 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11572, 11606, 96])).
% 2.86/3.04 tff(11608,plain,
% 2.86/3.04 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[479, 11607])).
% 2.86/3.04 tff(11609,plain,
% 2.86/3.04 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8053, 11608, 10693, 357])).
% 2.86/3.04 tff(11610,plain,
% 2.86/3.04 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[427, 11609])).
% 2.86/3.04 tff(11611,plain,
% 2.86/3.04 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[3673, 11608, 11590, 259])).
% 2.86/3.04 tff(11612,plain,
% 2.86/3.04 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[205, 11611])).
% 2.86/3.04 tff(11613,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[1163, 106, 260, 5609, 569, 501])).
% 2.86/3.04 tff(11614,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11615,plain,
% 2.86/3.04 ($false),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11614, 11612, 11610, 260, 11592])).
% 2.86/3.04 tff(11616,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.04 tff(11617,plain,
% 2.86/3.04 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11616, 259, 260, 11222])).
% 2.86/3.04 tff(11618,plain,
% 2.86/3.04 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9955, 11617])).
% 2.86/3.04 tff(11619,plain,
% 2.86/3.04 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[2312, 11618, 1998, 260])).
% 2.86/3.04 tff(11620,plain,
% 2.86/3.04 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[479, 11619])).
% 2.86/3.04 tff(11621,plain,
% 2.86/3.04 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8081, 171, 259, 10693, 11620])).
% 2.86/3.04 tff(11622,plain,
% 2.86/3.04 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[225, 11621])).
% 2.86/3.04 tff(11623,plain,
% 2.86/3.04 (~b(s(s(z)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11508, 11620, 11222])).
% 2.86/3.04 tff(11624,plain,
% 2.86/3.04 (r(s(s(z)), z)),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[157, 11623])).
% 2.86/3.04 tff(11625,plain,
% 2.86/3.04 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8650, 171, 259, 10693, 11620])).
% 2.86/3.04 tff(11626,plain,
% 2.86/3.04 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[205, 11625])).
% 2.86/3.04 tff(11627,plain,
% 2.86/3.04 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8123, 106, 260, 11622, 11626])).
% 2.86/3.04 tff(11628,plain,
% 2.86/3.04 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[9958, 11627])).
% 2.86/3.04 tff(11629,plain,
% 2.86/3.04 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[8131, 106, 260, 11622, 11626])).
% 2.86/3.04 tff(11630,plain,
% 2.86/3.04 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[351, 11629])).
% 2.86/3.04 tff(11631,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11632,plain,
% 2.86/3.04 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11633,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[11632])).
% 2.86/3.04 tff(11634,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[11633, 11631])).
% 2.86/3.04 tff(11635,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 2.86/3.04 inference(quant_inst,[status(thm)],[])).
% 2.86/3.04 tff(11636,plain,
% 2.86/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 2.86/3.04 inference(modus_ponens,[status(thm)],[11635, 11634])).
% 2.86/3.04 tff(11637,plain,
% 2.86/3.04 (~r(z, s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[11636, 106, 11222, 1998, 11618])).
% 2.86/3.04 tff(11638,plain,
% 2.86/3.04 (b(z, s(s(s(s(z)))))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[293, 11637])).
% 2.86/3.04 tff(11639,plain,
% 2.86/3.04 (~b(z, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[5981, 11638, 11630, 11628])).
% 2.86/3.04 tff(11640,plain,
% 2.86/3.04 (r(z, s(s(z)))),
% 2.86/3.04 inference(unit_resolution,[status(thm)],[124, 11639])).
% 2.86/3.04 tff(11641,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11642,plain,
% 2.86/3.04 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.04 inference(rewrite,[status(thm)],[])).
% 2.86/3.04 tff(11643,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))))),
% 2.86/3.04 inference(monotonicity,[status(thm)],[11642])).
% 2.86/3.04 tff(11644,plain,
% 2.86/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.04 inference(transitivity,[status(thm)],[11643, 11641])).
% 2.86/3.05 tff(11645,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11646,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11645, 11644])).
% 2.86/3.05 tff(11647,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11646, 106, 637, 600, 396, 1288])).
% 2.86/3.05 tff(11648,plain,((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11649,plain,
% 2.86/3.05 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11648, 11640, 11624, 11622])).
% 2.86/3.05 tff(11650,plain,
% 2.86/3.05 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[498, 11649])).
% 2.86/3.05 tff(11651,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[959, 11622, 11222, 11624])).
% 2.86/3.05 tff(11652,plain,
% 2.86/3.05 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[145, 11651])).
% 2.86/3.05 tff(11653,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11654,plain,
% 2.86/3.05 (((~b(s(s(s(s(s(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))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(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(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11655,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(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(s(s(s(s(z))))), z))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[11654])).
% 2.86/3.05 tff(11656,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(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(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[11655, 11653])).
% 2.86/3.05 tff(11657,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11658,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11657, 11656])).
% 2.86/3.05 tff(11659,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11658, 171, 9835, 10693, 11620, 11652, 11650])).
% 2.86/3.05 tff(11660,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11661,plain,
% 2.86/3.05 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11660, 11528, 1998])).
% 2.86/3.05 tff(11662,plain,
% 2.86/3.05 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[3668, 11661])).
% 2.86/3.05 tff(11663,plain,
% 2.86/3.05 (~b(z, s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11602, 11548, 11528])).
% 2.86/3.05 tff(11664,plain,
% 2.86/3.05 (r(z, s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[124, 11663])).
% 2.86/3.05 tff(11665,plain,
% 2.86/3.05 (~r(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10353, 11574, 11528, 11548, 11664, 11662])).
% 2.86/3.05 tff(11666,plain,
% 2.86/3.05 (b(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[157, 11665])).
% 2.86/3.05 tff(11667,plain,
% 2.86/3.05 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9104, 502, 10693, 1998, 11662])).
% 2.86/3.05 tff(11668,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[427, 11667])).
% 2.86/3.05 tff(11669,plain,
% 2.86/3.05 (~b(z, s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11133, 11666, 11528, 11662])).
% 2.86/3.05 tff(11670,plain,
% 2.86/3.05 (r(z, s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[293, 11669])).
% 2.86/3.05 tff(11671,plain,
% 2.86/3.05 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[7972, 5567, 5609, 569])).
% 2.86/3.05 tff(11672,plain,
% 2.86/3.05 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[498, 11671])).
% 2.86/3.05 tff(11673,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11095, 5567, 5609, 263])).
% 2.86/3.05 tff(11674,plain,
% 2.86/3.05 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[145, 11673])).
% 2.86/3.05 tff(11675,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11676,plain,
% 2.86/3.05 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11677,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[11676])).
% 2.86/3.05 tff(11678,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.05 inference(transitivity,[status(thm)],[11677, 11675])).
% 2.86/3.05 tff(11679,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11680,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11679, 11678])).
% 2.86/3.05 tff(11681,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11680, 171, 323, 1, 9835, 11674, 11672])).
% 2.86/3.05 tff(11682,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11683,plain,
% 2.86/3.05 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11682, 11670, 11668, 11666, 11548, 11576])).
% 2.86/3.05 tff(11684,plain,
% 2.86/3.05 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9955, 11683])).
% 2.86/3.05 tff(11685,plain,
% 2.86/3.05 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6512, 11684, 11528, 11548])).
% 2.86/3.05 tff(11686,plain,
% 2.86/3.05 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10009, 11684, 11664, 11574, 11576])).
% 2.86/3.05 tff(11687,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[351, 11686, 11685])).
% 2.86/3.05 tff(11688,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11689,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11688, 1998])).
% 2.86/3.05 tff(11690,plain,
% 2.86/3.05 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[479, 11689])).
% 2.86/3.05 tff(11691,plain,
% 2.86/3.05 (~b(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11508, 11690, 11222])).
% 2.86/3.05 tff(11692,plain,
% 2.86/3.05 (r(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[157, 11691])).
% 2.86/3.05 tff(11693,plain,
% 2.86/3.05 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[471, 171, 11548, 11528, 11690])).
% 2.86/3.05 tff(11694,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[225, 11693])).
% 2.86/3.05 tff(11695,plain,
% 2.86/3.05 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11648, 11694, 11664, 11692])).
% 2.86/3.05 tff(11696,plain,
% 2.86/3.05 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[498, 11695])).
% 2.86/3.05 tff(11697,plain,
% 2.86/3.05 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[959, 11694, 11222, 11692])).
% 2.86/3.05 tff(11698,plain,
% 2.86/3.05 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[145, 11697])).
% 2.86/3.05 tff(11699,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11506, 171, 9835, 11690, 11698, 11696])).
% 2.86/3.05 tff(11700,plain,(~r(s(z), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11701,plain,
% 2.86/3.05 (b(s(z), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1996, 11700])).
% 2.86/3.05 tff(11702,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8778, 171, 11701, 838, 10693, 4])).
% 2.86/3.05 tff(11703,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11704,plain,
% 2.86/3.05 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11703, 4])).
% 2.86/3.05 tff(11705,plain,
% 2.86/3.05 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[2614, 11704])).
% 2.86/3.05 tff(11706,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11707,plain,
% 2.86/3.05 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11708,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[11707])).
% 2.86/3.05 tff(11709,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[11708, 11706])).
% 2.86/3.05 tff(11710,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11711,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11710, 11709])).
% 2.86/3.05 tff(11712,plain,
% 2.86/3.05 (~r(z, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11711, 106, 11705, 10696, 9843])).
% 2.86/3.05 tff(11713,plain,
% 2.86/3.05 (b(z, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9192, 11712])).
% 2.86/3.05 tff(11714,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~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)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11715,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~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))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11714, 10441])).
% 2.86/3.05 tff(11716,plain,
% 2.86/3.05 (~r(s(s(s(z))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11715, 106, 11705, 10696, 9843])).
% 2.86/3.05 tff(11717,plain,
% 2.86/3.05 (b(s(s(s(z))), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10429, 11716])).
% 2.86/3.05 tff(11718,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11719,plain,
% 2.86/3.05 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11720,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[11719])).
% 2.86/3.05 tff(11721,plain,
% 2.86/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[11720, 11718])).
% 2.86/3.05 tff(11722,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11723,plain,
% 2.86/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11722, 11721])).
% 2.86/3.05 tff(11724,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11723, 171, 3281, 11701, 11717, 11713])).
% 2.86/3.05 tff(11725,plain,((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11726,plain,
% 2.86/3.05 (~b(z, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11725, 4])).
% 2.86/3.05 tff(11727,plain,
% 2.86/3.05 (r(z, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[93, 11726])).
% 2.86/3.05 tff(11728,plain,
% 2.86/3.05 (~b(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11488, 11727, 2, 4])).
% 2.86/3.05 tff(11729,plain,
% 2.86/3.05 (r(s(s(z)), z)),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[157, 11728])).
% 2.86/3.05 tff(11730,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11731,plain,
% 2.86/3.05 (((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.86/3.05 inference(rewrite,[status(thm)],[])).
% 2.86/3.05 tff(11732,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 2.86/3.05 inference(monotonicity,[status(thm)],[11731])).
% 2.86/3.05 tff(11733,plain,
% 2.86/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 2.86/3.05 inference(transitivity,[status(thm)],[11732, 11730])).
% 2.86/3.05 tff(11734,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.86/3.05 inference(quant_inst,[status(thm)],[])).
% 2.86/3.05 tff(11735,plain,
% 2.86/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(s(z))))))),
% 2.86/3.05 inference(modus_ponens,[status(thm)],[11734, 11733])).
% 2.86/3.05 tff(11736,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11735, 106, 96, 2, 637, 3])).
% 2.86/3.05 tff(11737,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11738,plain,
% 2.86/3.05 (~r(s(z), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11737, 11729, 2, 11727])).
% 2.86/3.05 tff(11739,plain,
% 2.86/3.05 (b(s(z), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9990, 11738])).
% 2.86/3.05 tff(11740,plain,
% 2.86/3.05 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9808, 11739, 10693, 4])).
% 2.86/3.05 tff(11741,plain,
% 2.86/3.05 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[3668, 11740])).
% 2.86/3.05 tff(11742,plain,
% 2.86/3.05 (~r(z, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9881, 554, 2, 637])).
% 2.86/3.05 tff(11743,plain,
% 2.86/3.05 (b(z, s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[93, 11742])).
% 2.86/3.05 tff(11744,plain,
% 2.86/3.05 (~b(s(s(s(z))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10448, 11743, 4])).
% 2.86/3.05 tff(11745,plain,
% 2.86/3.05 (r(s(s(s(z))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1173, 11744])).
% 2.86/3.05 tff(11746,plain,
% 2.86/3.05 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8053, 357, 10693, 4])).
% 2.86/3.05 tff(11747,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[427, 11746])).
% 2.86/3.05 tff(11748,plain,
% 2.86/3.05 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8762, 10700, 9843, 11747])).
% 2.86/3.05 tff(11749,plain,
% 2.86/3.05 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[2614, 11748])).
% 2.86/3.05 tff(11750,plain,
% 2.86/3.05 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8446, 11749, 10693, 11701])).
% 2.86/3.05 tff(11751,plain,
% 2.86/3.05 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1368, 11750])).
% 2.86/3.05 tff(11752,plain,
% 2.86/3.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8834, 11751, 10700, 11747])).
% 2.86/3.05 tff(11753,plain,
% 2.86/3.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10361, 11752])).
% 2.86/3.05 tff(11754,plain,
% 2.86/3.05 (~r(z, s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[5649, 11747, 10696, 10700])).
% 2.86/3.05 tff(11755,plain,
% 2.86/3.05 (b(z, s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[293, 11754])).
% 2.86/3.05 tff(11756,plain,
% 2.86/3.05 (~b(s(s(s(z))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10448, 3281, 4])).
% 2.86/3.05 tff(11757,plain,
% 2.86/3.05 (r(s(s(s(z))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[1173, 11756])).
% 2.86/3.05 tff(11758,plain,
% 2.86/3.05 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[8843, 11751, 11757, 11747])).
% 2.86/3.05 tff(11759,plain,
% 2.86/3.05 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[6475, 11758])).
% 2.86/3.05 tff(11760,plain,
% 2.86/3.05 (~r(z, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10522, 11751, 11757, 10696])).
% 2.86/3.05 tff(11761,plain,
% 2.86/3.05 (b(z, s(s(s(z))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9192, 11760])).
% 2.86/3.05 tff(11762,plain,
% 2.86/3.05 ($false),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9700, 11761, 11759, 11749, 11755, 11753])).
% 2.86/3.05 tff(11763,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.05 tff(11764,plain,
% 2.86/3.05 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11763, 11743, 4])).
% 2.86/3.05 tff(11765,plain,
% 2.86/3.05 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[9955, 11764])).
% 2.86/3.05 tff(11766,plain,
% 2.86/3.05 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[11395, 11765, 554, 11745])).
% 2.86/3.05 tff(11767,plain,
% 2.86/3.05 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.05 inference(unit_resolution,[status(thm)],[10361, 11766])).
% 2.86/3.05 tff(11768,plain,
% 2.86/3.05 (~b(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9841, 171, 11743, 9835, 4])).
% 2.86/3.06 tff(11769,plain,
% 2.86/3.06 (r(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[498, 11768])).
% 2.86/3.06 tff(11770,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10694, 11743, 10693])).
% 2.86/3.06 tff(11771,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[145, 11770])).
% 2.86/3.06 tff(11772,plain,
% 2.86/3.06 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10410, 106, 637, 11771, 11769])).
% 2.86/3.06 tff(11773,plain,
% 2.86/3.06 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[205, 11772])).
% 2.86/3.06 tff(11774,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10398, 11743, 4, 637])).
% 2.86/3.06 tff(11775,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[225, 11774])).
% 2.86/3.06 tff(11776,plain,
% 2.86/3.06 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9808, 3686, 10693, 4])).
% 2.86/3.06 tff(11777,plain,
% 2.86/3.06 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9990, 11776])).
% 2.86/3.06 tff(11778,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9958, 5783])).
% 2.86/3.06 tff(11779,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6011, 11778, 11777, 2, 263])).
% 2.86/3.06 tff(11780,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), 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(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11781,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11780, 11765, 2, 11775, 11773, 4])).
% 2.86/3.06 tff(11782,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[3668, 11781])).
% 2.86/3.06 tff(11783,plain,
% 2.86/3.06 (~r(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9423, 106, 11782, 11771, 11769])).
% 2.86/3.06 tff(11784,plain,
% 2.86/3.06 (b(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[293, 11783])).
% 2.86/3.06 tff(11785,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9418, 106, 11782, 11771, 11769])).
% 2.86/3.06 tff(11786,plain,
% 2.86/3.06 (b(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[274, 11785])).
% 2.86/3.06 tff(11787,plain,
% 2.86/3.06 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10708, 171, 11743, 9835, 11786])).
% 2.86/3.06 tff(11788,plain,
% 2.86/3.06 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9990, 11787])).
% 2.86/3.06 tff(11789,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6011, 11788, 2, 11765])).
% 2.86/3.06 tff(11790,plain,
% 2.86/3.06 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9958, 11789])).
% 2.86/3.06 tff(11791,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11792,plain,
% 2.86/3.06 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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(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))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11793,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[11792])).
% 2.86/3.06 tff(11794,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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)))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[11793, 11791])).
% 2.86/3.06 tff(11795,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(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)))))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(11796,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[11795, 11794])).
% 2.86/3.06 tff(11797,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11796, 171, 11773, 11775, 11790])).
% 2.86/3.06 tff(11798,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[427, 11797])).
% 2.86/3.06 tff(11799,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8762, 11798, 11769, 11782])).
% 2.86/3.06 tff(11800,plain,
% 2.86/3.06 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2614, 11799])).
% 2.86/3.06 tff(11801,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8446, 11800, 10693, 11701])).
% 2.86/3.06 tff(11802,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1368, 11801])).
% 2.86/3.06 tff(11803,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8843, 11802, 11745, 11798])).
% 2.86/3.06 tff(11804,plain,
% 2.86/3.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6475, 11803])).
% 2.86/3.06 tff(11805,plain,
% 2.86/3.06 (~r(z, s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10522, 11802, 11745, 11771])).
% 2.86/3.06 tff(11806,plain,
% 2.86/3.06 (b(z, s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9192, 11805])).
% 2.86/3.06 tff(11807,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9700, 11806, 11804, 11800, 11784, 11767])).
% 2.86/3.06 tff(11808,plain,((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11809,plain,
% 2.86/3.06 (~r(s(z), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11808, 11729, 4, 2])).
% 2.86/3.06 tff(11810,plain,
% 2.86/3.06 (b(s(z), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[550, 11809])).
% 2.86/3.06 tff(11811,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8744, 106, 260, 11747, 11705])).
% 2.86/3.06 tff(11812,plain,
% 2.86/3.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10361, 11811])).
% 2.86/3.06 tff(11813,plain,
% 2.86/3.06 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8752, 106, 260, 11747, 11705])).
% 2.86/3.06 tff(11814,plain,
% 2.86/3.06 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6475, 11813])).
% 2.86/3.06 tff(11815,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11816,plain,
% 2.86/3.06 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11817,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[11816])).
% 2.86/3.06 tff(11818,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[11817, 11815])).
% 2.86/3.06 tff(11819,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(11820,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[11819, 11818])).
% 2.86/3.06 tff(11821,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11820, 171, 11701, 11814, 11812, 357])).
% 2.86/3.06 tff(11822,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11823,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11822, 11741, 4])).
% 2.86/3.06 tff(11824,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9955, 11823])).
% 2.86/3.06 tff(11825,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8762, 5609, 1288, 260])).
% 2.86/3.06 tff(11826,plain,
% 2.86/3.06 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[2614, 11825])).
% 2.86/3.06 tff(11827,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8446, 11826, 10693, 11701])).
% 2.86/3.06 tff(11828,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1368, 11827])).
% 2.86/3.06 tff(11829,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8834, 11828, 260, 5609])).
% 2.86/3.06 tff(11830,plain,
% 2.86/3.06 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10361, 11829])).
% 2.86/3.06 tff(11831,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8853, 11830, 376, 11826, 11701])).
% 2.86/3.06 tff(11832,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6475, 11831])).
% 2.86/3.06 tff(11833,plain,
% 2.86/3.06 (~r(s(s(s(z))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8843, 11832, 11828, 5609])).
% 2.86/3.06 tff(11834,plain,
% 2.86/3.06 (b(s(s(s(z))), s(z))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[1173, 11833])).
% 2.86/3.06 tff(11835,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9041, 171, 323, 11834, 11826, 10693, 4])).
% 2.86/3.06 tff(11836,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11837,plain,
% 2.86/3.06 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11836, 5609, 4, 323, 260, 376])).
% 2.86/3.06 tff(11838,plain,
% 2.86/3.06 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[498, 11837])).
% 2.86/3.06 tff(11839,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11658, 171, 9835, 10693, 4, 159, 1313])).
% 2.86/3.06 tff(11840,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11841,plain,
% 2.86/3.06 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11840, 11838, 4])).
% 2.86/3.06 tff(11842,plain,
% 2.86/3.06 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[145, 11841])).
% 2.86/3.06 tff(11843,plain,
% 2.86/3.06 (~r(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11095, 11842, 5609, 263])).
% 2.86/3.06 tff(11844,plain,
% 2.86/3.06 (b(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[293, 11843])).
% 2.86/3.06 tff(11845,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11846,plain,
% 2.86/3.06 (((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11847,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[11846])).
% 2.86/3.06 tff(11848,plain,
% 2.86/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.06 inference(transitivity,[status(thm)],[11847, 11845])).
% 2.86/3.06 tff(11849,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(11850,plain,
% 2.86/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[11849, 11848])).
% 2.86/3.06 tff(11851,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11850, 171, 9835, 10693, 4, 376, 11838, 11844])).
% 2.86/3.06 tff(11852,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11853,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11852, 11824, 11739, 4, 11810, 11741])).
% 2.86/3.06 tff(11854,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[427, 11853])).
% 2.86/3.06 tff(11855,plain,
% 2.86/3.06 (~r(s(z), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11808, 637, 4, 2])).
% 2.86/3.06 tff(11856,plain,
% 2.86/3.06 (b(s(z), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[550, 11855])).
% 2.86/3.06 tff(11857,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[959, 396, 96, 637])).
% 2.86/3.06 tff(11858,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[145, 11857])).
% 2.86/3.06 tff(11859,plain,
% 2.86/3.06 (~b(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11840, 11858, 4])).
% 2.86/3.06 tff(11860,plain,
% 2.86/3.06 (r(z, s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[498, 11859])).
% 2.86/3.06 tff(11861,plain,
% 2.86/3.06 (~r(z, s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11648, 11860, 396, 637])).
% 2.86/3.06 tff(11862,plain,
% 2.86/3.06 (b(z, s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[124, 11861])).
% 2.86/3.06 tff(11863,plain,
% 2.86/3.06 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8135, 11862, 260, 11860, 396])).
% 2.86/3.06 tff(11864,plain,
% 2.86/3.06 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[205, 11863])).
% 2.86/3.06 tff(11865,plain,
% 2.86/3.06 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11836, 376, 4, 323, 260, 1288])).
% 2.86/3.06 tff(11866,plain,
% 2.86/3.06 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[427, 11865])).
% 2.86/3.06 tff(11867,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[8157, 171, 323, 161, 83, 4, 376, 2141])).
% 2.86/3.06 tff(11868,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(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))))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11869,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11868, 11866, 161, 323, 4, 376])).
% 2.86/3.06 tff(11870,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[274, 11869])).
% 2.86/3.06 tff(11871,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11868, 83, 161, 323, 4, 376])).
% 2.86/3.06 tff(11872,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), z)),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[274, 11871])).
% 2.86/3.06 tff(11873,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11874,plain,
% 2.86/3.06 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.86/3.06 inference(rewrite,[status(thm)],[])).
% 2.86/3.06 tff(11875,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 2.86/3.06 inference(monotonicity,[status(thm)],[11874])).
% 2.86/3.06 tff(11876,plain,
% 2.86/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 2.86/3.06 inference(transitivity,[status(thm)],[11875, 11873])).
% 2.86/3.06 tff(11877,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.06 inference(quant_inst,[status(thm)],[])).
% 2.86/3.06 tff(11878,plain,
% 2.86/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 2.86/3.06 inference(modus_ponens,[status(thm)],[11877, 11876])).
% 2.86/3.06 tff(11879,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11878, 106, 96, 637, 2118, 500])).
% 2.86/3.06 tff(11880,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11881,plain,
% 2.86/3.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11880, 11872, 637, 96])).
% 2.86/3.06 tff(11882,plain,
% 2.86/3.06 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[351, 11881])).
% 2.86/3.06 tff(11883,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11045, 171, 83, 160, 356, 11882])).
% 2.86/3.06 tff(11884,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11885,plain,
% 2.86/3.06 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11884, 11866, 160, 637, 96, 161, 323, 4, 376])).
% 2.86/3.06 tff(11886,plain,
% 2.86/3.06 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9958, 11885])).
% 2.86/3.06 tff(11887,plain,
% 2.86/3.06 ($false),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[6904, 11886, 11870, 96, 637])).
% 2.86/3.06 tff(11888,plain,((~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.06 tff(11889,plain,
% 2.86/3.06 (~b(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[11888, 11864, 637, 96, 11862, 11856, 4, 260, 11860])).
% 2.86/3.06 tff(11890,plain,
% 2.86/3.06 (r(s(z), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[9990, 11889])).
% 2.86/3.06 tff(11891,plain,
% 2.86/3.06 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[5971, 11890, 260, 2])).
% 2.86/3.06 tff(11892,plain,
% 2.86/3.06 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[351, 11891])).
% 2.86/3.06 tff(11893,plain,
% 2.86/3.06 (~r(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[10152, 11890, 260, 96])).
% 2.86/3.06 tff(11894,plain,
% 2.86/3.06 (b(z, s(s(s(s(z)))))),
% 2.86/3.06 inference(unit_resolution,[status(thm)],[293, 11893])).
% 2.86/3.07 tff(11895,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[5981, 11894, 11862, 11892])).
% 2.86/3.07 tff(11896,plain,
% 2.86/3.07 (r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9958, 11895])).
% 2.86/3.07 tff(11897,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6904, 569, 96, 637])).
% 2.86/3.07 tff(11898,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[274, 11897])).
% 2.86/3.07 tff(11899,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11900,plain,
% 2.86/3.07 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11901,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11900])).
% 2.86/3.07 tff(11902,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11901, 11899])).
% 2.86/3.07 tff(11903,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11904,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11903, 11902])).
% 2.86/3.07 tff(11905,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11904, 171, 9835, 357, 2527, 2141])).
% 2.86/3.07 tff(11906,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11907,plain,
% 2.86/3.07 (~b(z, s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11906, 11898, 357])).
% 2.86/3.07 tff(11908,plain,
% 2.86/3.07 (r(z, s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[293, 11907])).
% 2.86/3.07 tff(11909,plain,
% 2.86/3.07 (~r(z, s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[7972, 11908, 11747, 569])).
% 2.86/3.07 tff(11910,plain,
% 2.86/3.07 (b(z, s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[498, 11909])).
% 2.86/3.07 tff(11911,plain,
% 2.86/3.07 (~r(z, s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6247, 11908, 637, 569])).
% 2.86/3.07 tff(11912,plain,
% 2.86/3.07 (b(z, s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[124, 11911])).
% 2.86/3.07 tff(11913,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11914,plain,
% 2.86/3.07 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11915,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11914])).
% 2.86/3.07 tff(11916,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11915, 11913])).
% 2.86/3.07 tff(11917,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), z)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11918,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11917, 11916])).
% 2.86/3.07 tff(11919,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11918, 171, 323, 11912, 9835, 10693, 4, 11910])).
% 2.86/3.07 tff(11920,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11921,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11920, 11896, 4, 637, 11856, 96])).
% 2.86/3.07 tff(11922,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6011, 11896, 2, 11890])).
% 2.86/3.07 tff(11923,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9955, 11922, 11921])).
% 2.86/3.07 tff(11924,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11925,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11924, 11741, 4, 11727, 2, 11729])).
% 2.86/3.07 tff(11926,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[225, 11925])).
% 2.86/3.07 tff(11927,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6904, 569, 11727, 637])).
% 2.86/3.07 tff(11928,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[274, 11927])).
% 2.86/3.07 tff(11929,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9808, 376, 10693, 4])).
% 2.86/3.07 tff(11930,plain,
% 2.86/3.07 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[3668, 11929])).
% 2.86/3.07 tff(11931,plain,
% 2.86/3.07 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11822, 11930, 4])).
% 2.86/3.07 tff(11932,plain,
% 2.86/3.07 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9955, 11931])).
% 2.86/3.07 tff(11933,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11852, 11932, 376, 4, 323, 11930])).
% 2.86/3.07 tff(11934,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[427, 11933])).
% 2.86/3.07 tff(11935,plain,
% 2.86/3.07 (~r(z, s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6247, 569, 637, 5567])).
% 2.86/3.07 tff(11936,plain,
% 2.86/3.07 (b(z, s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[124, 11935])).
% 2.86/3.07 tff(11937,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11868, 11936, 11928, 11934, 323, 4, 376])).
% 2.86/3.07 tff(11938,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11939,plain,
% 2.86/3.07 (~r(z, s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11938, 569, 4, 376, 637, 323])).
% 2.86/3.07 tff(11940,plain,
% 2.86/3.07 (b(z, s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[293, 11939])).
% 2.86/3.07 tff(11941,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[10202, 171, 9835, 376, 11940, 11928])).
% 2.86/3.07 tff(11942,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11943,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11942, 11739, 4, 11729, 11810])).
% 2.86/3.07 tff(11944,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9958, 11943])).
% 2.86/3.07 tff(11945,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9393, 171, 83, 207, 356, 2352])).
% 2.86/3.07 tff(11946,plain,((~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))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11947,plain,
% 2.86/3.07 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11946, 11944, 11926, 11854])).
% 2.86/3.07 tff(11948,plain,
% 2.86/3.07 (r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[351, 11947])).
% 2.86/3.07 tff(11949,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11880, 11948, 11729, 11727])).
% 2.86/3.07 tff(11950,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[274, 11949])).
% 2.86/3.07 tff(11951,plain,
% 2.86/3.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11437, 106, 260, 2604, 1357])).
% 2.86/3.07 tff(11952,plain,
% 2.86/3.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[10361, 11951])).
% 2.86/3.07 tff(11953,plain,
% 2.86/3.07 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11252, 1357, 2604, 260])).
% 2.86/3.07 tff(11954,plain,
% 2.86/3.07 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[6475, 11953])).
% 2.86/3.07 tff(11955,plain,
% 2.86/3.07 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(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)))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11956,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(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))))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11955])).
% 2.86/3.07 tff(11957,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(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)))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11956, 8556])).
% 2.86/3.07 tff(11958,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11959,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11958, 11957])).
% 2.86/3.07 tff(11960,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11959, 171, 11701, 376, 11954, 11952])).
% 2.86/3.07 tff(11961,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11962,plain,
% 2.86/3.07 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11961, 11739, 11741, 11705])).
% 2.86/3.07 tff(11963,plain,
% 2.86/3.07 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[1368, 11962])).
% 2.86/3.07 tff(11964,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11965,plain,
% 2.86/3.07 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(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)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11966,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11965])).
% 2.86/3.07 tff(11967,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11966, 11964])).
% 2.86/3.07 tff(11968,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11969,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11968, 11967])).
% 2.86/3.07 tff(11970,plain,
% 2.86/3.07 (~r(z, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11969, 106, 260, 5567, 2828])).
% 2.86/3.07 tff(11971,plain,
% 2.86/3.07 (b(z, s(s(s(z))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[9192, 11970])).
% 2.86/3.07 tff(11972,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11973,plain,
% 2.86/3.07 (((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11974,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11973])).
% 2.86/3.07 tff(11975,plain,
% 2.86/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11974, 11972])).
% 2.86/3.07 tff(11976,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), z)))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11977,plain,
% 2.86/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), z))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11976, 11975])).
% 2.86/3.07 tff(11978,plain,
% 2.86/3.07 (~r(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11977, 106, 260, 5567, 2828])).
% 2.86/3.07 tff(11979,plain,
% 2.86/3.07 (b(s(s(s(z))), z)),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[10429, 11978])).
% 2.86/3.07 tff(11980,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11364, 171, 11701, 1384, 4, 11979, 11971])).
% 2.86/3.07 tff(11981,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11982,plain,
% 2.86/3.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11981, 1384, 4, 260, 5567])).
% 2.86/3.07 tff(11983,plain,
% 2.86/3.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[10361, 11982])).
% 2.86/3.07 tff(11984,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11985,plain,
% 2.86/3.07 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(rewrite,[status(thm)],[])).
% 2.86/3.07 tff(11986,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.86/3.07 inference(monotonicity,[status(thm)],[11985])).
% 2.86/3.07 tff(11987,plain,
% 2.86/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(transitivity,[status(thm)],[11986, 11984])).
% 2.86/3.07 tff(11988,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.07 inference(quant_inst,[status(thm)],[])).
% 2.86/3.07 tff(11989,plain,
% 2.86/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.07 inference(modus_ponens,[status(thm)],[11988, 11987])).
% 2.86/3.07 tff(11990,plain,
% 2.86/3.07 ($false),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11989, 171, 9835, 11701, 1384, 4, 11983, 2141])).
% 2.86/3.07 tff(11991,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.07 tff(11992,plain,
% 2.86/3.07 (~r(z, s(s(s(s(z)))))),
% 2.86/3.07 inference(unit_resolution,[status(thm)],[11991, 11963, 4, 11741, 11950])).
% 2.86/3.07 tff(11993,plain,
% 2.86/3.07 (b(z, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[293, 11992])).
% 2.86/3.08 tff(11994,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10202, 171, 9835, 11739, 11993, 11950])).
% 2.86/3.08 tff(11995,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(11996,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11995, 2])).
% 2.86/3.08 tff(11997,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[479, 11996])).
% 2.86/3.08 tff(11998,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8476, 106, 2, 11997, 3, 501])).
% 2.86/3.08 tff(11999,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12000,plain,
% 2.86/3.08 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11999, 3, 2])).
% 2.86/3.08 tff(12001,plain,
% 2.86/3.08 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[205, 12000])).
% 2.86/3.08 tff(12002,plain,
% 2.86/3.08 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8468, 3, 2, 11997])).
% 2.86/3.08 tff(12003,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[225, 12002])).
% 2.86/3.08 tff(12004,plain,
% 2.86/3.08 (~b(s(z), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8497, 171, 10693, 12001, 12003])).
% 2.86/3.08 tff(12005,plain,
% 2.86/3.08 (r(s(z), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[550, 12004])).
% 2.86/3.08 tff(12006,plain,
% 2.86/3.08 (~r(z, s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11572, 3, 502])).
% 2.86/3.08 tff(12007,plain,
% 2.86/3.08 (b(z, s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[93, 12006])).
% 2.86/3.08 tff(12008,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[7068, 5609, 502, 3])).
% 2.86/3.08 tff(12009,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3668, 12008])).
% 2.86/3.08 tff(12010,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[7054, 5609, 502, 554])).
% 2.86/3.08 tff(12011,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9955, 12010])).
% 2.86/3.08 tff(12012,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9676, 12011, 12009, 10693, 12007])).
% 2.86/3.08 tff(12013,plain,((~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(z)))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12014,plain,
% 2.86/3.08 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12013, 12005, 11997, 3])).
% 2.86/3.08 tff(12015,plain,
% 2.86/3.08 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[427, 12014])).
% 2.86/3.08 tff(12016,plain,
% 2.86/3.08 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8483, 12015, 10693, 12003, 12001, 3, 2])).
% 2.86/3.08 tff(12017,plain,
% 2.86/3.08 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[3668, 12016])).
% 2.86/3.08 tff(12018,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8203, 12017, 11997, 3])).
% 2.86/3.08 tff(12019,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9955, 12018])).
% 2.86/3.08 tff(12020,plain,
% 2.86/3.08 (~r(z, s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11572, 3, 11997])).
% 2.86/3.08 tff(12021,plain,
% 2.86/3.08 (b(z, s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[93, 12020])).
% 2.86/3.08 tff(12022,plain,
% 2.86/3.08 (~r(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9352, 12005, 11997, 2])).
% 2.86/3.08 tff(12023,plain,
% 2.86/3.08 (b(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1173, 12022])).
% 2.86/3.08 tff(12024,plain,
% 2.86/3.08 (~b(s(s(s(z))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10424, 12023, 12021])).
% 2.86/3.08 tff(12025,plain,
% 2.86/3.08 (r(s(s(s(z))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10429, 12024])).
% 2.86/3.08 tff(12026,plain,
% 2.86/3.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10579, 12019, 12021, 12025])).
% 2.86/3.08 tff(12027,plain,
% 2.86/3.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10361, 12026])).
% 2.86/3.08 tff(12028,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12029,plain,
% 2.86/3.08 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12030,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12029])).
% 2.86/3.08 tff(12031,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), 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(s(z))), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12030, 12028])).
% 2.86/3.08 tff(12032,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12033,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12032, 12031])).
% 2.86/3.08 tff(12034,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12033, 171, 1188, 838, 10693, 160, 207])).
% 2.86/3.08 tff(12035,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12036,plain,
% 2.86/3.08 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12035, 12023, 12001, 12003])).
% 2.86/3.08 tff(12037,plain,
% 2.86/3.08 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2614, 12036])).
% 2.86/3.08 tff(12038,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9195, 12037, 11997, 12017])).
% 2.86/3.08 tff(12039,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[6475, 12038])).
% 2.86/3.08 tff(12040,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11820, 171, 11701, 12039, 12027, 12019])).
% 2.86/3.08 tff(12041,plain,((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12042,plain,
% 2.86/3.08 (~r(s(z), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12041, 2])).
% 2.86/3.08 tff(12043,plain,
% 2.86/3.08 (b(s(z), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9990, 12042])).
% 2.86/3.08 tff(12044,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8521, 3686, 10693, 12043])).
% 2.86/3.08 tff(12045,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[427, 12044])).
% 2.86/3.08 tff(12046,plain,
% 2.86/3.08 (~b(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9676, 3281, 10693, 3686])).
% 2.86/3.08 tff(12047,plain,
% 2.86/3.08 (r(s(s(s(s(z)))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9955, 12046])).
% 2.86/3.08 tff(12048,plain,
% 2.86/3.08 (~r(s(z), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[7054, 12047, 11997, 12045])).
% 2.86/3.08 tff(12049,plain,
% 2.86/3.08 (b(s(z), s(s(z)))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[550, 12048])).
% 2.86/3.08 tff(12050,plain,
% 2.86/3.08 (~b(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10237, 12049, 3281])).
% 2.86/3.08 tff(12051,plain,
% 2.86/3.08 (r(s(s(z)), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[157, 12050])).
% 2.86/3.08 tff(12052,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12053,plain,
% 2.86/3.08 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12054,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z)))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12053])).
% 2.86/3.08 tff(12055,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z))))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12054, 12052])).
% 2.86/3.08 tff(12056,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12057,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(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(z), s(s(s(s(s(z)))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12056, 12055])).
% 2.86/3.08 tff(12058,plain,
% 2.86/3.08 (~b(s(s(s(s(z)))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12057, 171, 3281, 9835, 3686, 10693, 12043])).
% 2.86/3.08 tff(12059,plain,
% 2.86/3.08 (r(s(s(s(s(z)))), z)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[274, 12058])).
% 2.86/3.08 tff(12060,plain,
% 2.86/3.08 (~r(z, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[11095, 10696, 12045, 12047])).
% 2.86/3.08 tff(12061,plain,
% 2.86/3.08 (b(z, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[293, 12060])).
% 2.86/3.08 tff(12062,plain,
% 2.86/3.08 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10690, 12061, 11701, 12043, 3686, 3281])).
% 2.86/3.08 tff(12063,plain,
% 2.86/3.08 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1368, 12062])).
% 2.86/3.08 tff(12064,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12065,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12066,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12065, 12064])).
% 2.86/3.08 tff(12067,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12066, 106, 5609, 1357, 263, 2828])).
% 2.86/3.08 tff(12068,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12069,plain,
% 2.86/3.08 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12068, 12063, 12045, 12047])).
% 2.86/3.08 tff(12070,plain,
% 2.86/3.08 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10361, 12069])).
% 2.86/3.08 tff(12071,plain,
% 2.86/3.08 (~b(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10927, 12059, 3281, 12047, 2])).
% 2.86/3.08 tff(12072,plain,
% 2.86/3.08 (r(s(s(s(z))), s(z))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[1173, 12071])).
% 2.86/3.08 tff(12073,plain,
% 2.86/3.08 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8843, 12072, 12045, 12063])).
% 2.86/3.08 tff(12074,plain,
% 2.86/3.08 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[6475, 12073])).
% 2.86/3.08 tff(12075,plain,
% 2.86/3.08 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[8853, 12074, 12043, 12070, 11701])).
% 2.86/3.08 tff(12076,plain,
% 2.86/3.08 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2614, 12075])).
% 2.86/3.08 tff(12077,plain,
% 2.86/3.08 (~r(z, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[10522, 12072, 10696, 12063])).
% 2.86/3.08 tff(12078,plain,
% 2.86/3.08 (b(z, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[672])).
% 2.86/3.08 tff(12079,plain,
% 2.86/3.08 (b(elem!1, s(s(s(s(z))))) <=> b(z, s(s(s(s(z)))))),
% 2.86/3.08 inference(symmetry,[status(thm)],[12078])).
% 2.86/3.08 tff(12080,plain,
% 2.86/3.08 ((~b(elem!1, s(s(s(s(z)))))) <=> (~b(z, s(s(s(s(z))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12079])).
% 2.86/3.08 tff(12081,plain,
% 2.86/3.08 (~b(z, s(s(s(s(z)))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[4093, 12080])).
% 2.86/3.08 tff(12082,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[2527, 12081])).
% 2.86/3.08 tff(12083,plain,((~(z = elem!1)) | (~b(z, s(s(s(s(z)))))) | b(elem!1, s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12084,plain,
% 2.86/3.08 (b(elem!1, s(s(s(s(z)))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12083, 672, 2527])).
% 2.86/3.08 tff(12085,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12086,plain,
% 2.86/3.08 (((~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(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12087,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 2.86/3.08 inference(monotonicity,[status(thm)],[12086])).
% 2.86/3.08 tff(12088,plain,
% 2.86/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.86/3.08 inference(transitivity,[status(thm)],[12087, 12085])).
% 2.86/3.08 tff(12089,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))))),
% 2.86/3.08 inference(quant_inst,[status(thm)],[])).
% 2.86/3.08 tff(12090,plain,
% 2.86/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12089, 12088])).
% 2.86/3.08 tff(12091,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12090, 171, 2038, 6462, 2433, 2852])).
% 2.86/3.08 tff(12092,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12093,plain,
% 2.86/3.08 (~b(elem!1, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12092, 12084, 2852, 6462])).
% 2.86/3.08 tff(12094,plain,
% 2.86/3.08 (~b(elem!1, s(s(s(elem!1))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[948, 12093, 1930])).
% 2.86/3.08 tff(12095,plain,
% 2.86/3.08 (r(elem!1, s(s(s(z))))),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[942, 12094, 1930])).
% 2.86/3.08 tff(12096,plain,
% 2.86/3.08 (r(z, s(s(s(z))))),
% 2.86/3.08 inference(modus_ponens,[status(thm)],[12095, 1962])).
% 2.86/3.08 tff(12097,plain,
% 2.86/3.08 ($false),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[9190, 12096])).
% 2.86/3.08 tff(12098,plain,((~(z = elem!1)) | r(z, s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.08 tff(12099,plain,
% 2.86/3.08 (~(z = elem!1)),
% 2.86/3.08 inference(unit_resolution,[status(thm)],[12098, 12074, 12061, 12077, 12070])).
% 2.86/3.08 tff(12100,plain,
% 2.86/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.08 inference(rewrite,[status(thm)],[])).
% 2.86/3.08 tff(12101,plain,
% 2.86/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12102,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12101, 12100])).
% 2.86/3.09 tff(12103,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12102, 106, 638, 637, 396, 127])).
% 2.86/3.09 tff(12104,plain,((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(12105,plain,
% 2.86/3.09 (~r(z, elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12104, 396, 12051, 10696])).
% 2.86/3.09 tff(12106,plain,
% 2.86/3.09 (b(z, elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[651, 12105, 12099])).
% 2.86/3.09 tff(12107,plain,
% 2.86/3.09 (s(s(s(s(z)))) = s(elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[785])).
% 2.86/3.09 tff(12108,plain,
% 2.86/3.09 (b(z, s(s(s(s(z))))) <=> b(z, s(elem!1))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12107])).
% 2.86/3.09 tff(12109,plain,
% 2.86/3.09 (b(z, s(elem!1))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[2527, 12108])).
% 2.86/3.09 tff(12110,plain,
% 2.86/3.09 (s(elem!1) = s(s(s(s(z))))),
% 2.86/3.09 inference(symmetry,[status(thm)],[12107])).
% 2.86/3.09 tff(12111,plain,
% 2.86/3.09 (b(elem!1, s(elem!1)) <=> b(elem!1, s(s(s(s(z)))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12110])).
% 2.86/3.09 tff(12112,plain,
% 2.86/3.09 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(elem!1))),
% 2.86/3.09 inference(symmetry,[status(thm)],[12111])).
% 2.86/3.09 tff(12113,plain,
% 2.86/3.09 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[785])).
% 2.86/3.09 tff(12114,plain,
% 2.86/3.09 (b(elem!1, s(s(s(s(z)))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[2852, 12113])).
% 2.86/3.09 tff(12115,plain,
% 2.86/3.09 (b(elem!1, s(elem!1))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12114, 12112])).
% 2.86/3.09 tff(12116,plain,
% 2.86/3.09 (b(s(elem!1), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12110])).
% 2.86/3.09 tff(12117,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), elem!1) <=> b(s(elem!1), elem!1)),
% 2.86/3.09 inference(symmetry,[status(thm)],[12116])).
% 2.86/3.09 tff(12118,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(z)))), elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[785])).
% 2.86/3.09 tff(12119,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), elem!1)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[6462, 12118])).
% 2.86/3.09 tff(12120,plain,
% 2.86/3.09 (b(s(elem!1), elem!1)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12119, 12117])).
% 2.86/3.09 tff(12121,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12122,plain,
% 2.86/3.09 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12123,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12122])).
% 2.86/3.09 tff(12124,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)))),
% 2.86/3.09 inference(transitivity,[status(thm)],[12123, 12121])).
% 2.86/3.09 tff(12125,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12126,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12125, 12124])).
% 2.86/3.09 tff(12127,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12126, 171, 3137, 12120, 12115, 12109])).
% 2.86/3.09 tff(12128,plain,((~(s(s(s(z))) = elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(12129,plain,
% 2.86/3.09 (~(s(s(s(z))) = elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12128, 12106, 12074, 12070, 12061])).
% 2.86/3.09 tff(12130,plain,
% 2.86/3.09 (~r(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[9538, 12047, 11997, 12045])).
% 2.86/3.09 tff(12131,plain,
% 2.86/3.09 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[1435])).
% 2.86/3.09 tff(12132,plain,
% 2.86/3.09 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 2.86/3.09 inference(symmetry,[status(thm)],[12131])).
% 2.86/3.09 tff(12133,plain,
% 2.86/3.09 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12132])).
% 2.86/3.09 tff(12134,plain,
% 2.86/3.09 (~r(elem!1, s(z))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[3996, 12133])).
% 2.86/3.09 tff(12135,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[2339])).
% 2.86/3.09 tff(12136,plain,
% 2.86/3.09 ((~b(s(s(s(s(z)))), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12135])).
% 2.86/3.09 tff(12137,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[1435])).
% 2.86/3.09 tff(12138,plain,
% 2.86/3.09 ((~b(s(s(s(s(z)))), s(z))) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12137])).
% 2.86/3.09 tff(12139,plain,
% 2.86/3.09 (~b(s(s(s(s(z)))), elem!1)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[315, 12138])).
% 2.86/3.09 tff(12140,plain,
% 2.86/3.09 (~b(s(s(s(elem!1))), elem!1)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12139, 12136])).
% 2.86/3.09 tff(12141,plain,
% 2.86/3.09 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.86/3.09 inference(monotonicity,[status(thm)],[2339])).
% 2.86/3.09 tff(12142,plain,
% 2.86/3.09 ((~b(s(s(s(s(z)))), z)) <=> (~b(s(s(s(elem!1))), z))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12141])).
% 2.86/3.09 tff(12143,plain,
% 2.86/3.09 (~b(s(s(s(elem!1))), z)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[268, 12142])).
% 2.86/3.09 tff(12144,plain,
% 2.86/3.09 (b(s(z), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[30, 6])).
% 2.86/3.09 tff(12145,plain,
% 2.86/3.09 (r(s(s(z)), s(z)) <=> r(elem!1, s(z))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[1418])).
% 2.86/3.09 tff(12146,plain,
% 2.86/3.09 (r(elem!1, s(z)) <=> r(s(s(z)), s(z))),
% 2.86/3.09 inference(symmetry,[status(thm)],[12145])).
% 2.86/3.09 tff(12147,plain,
% 2.86/3.09 ((~r(elem!1, s(z))) <=> (~r(s(s(z)), s(z)))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12146])).
% 2.86/3.09 tff(12148,plain,
% 2.86/3.09 (~r(s(s(z)), s(z))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[676, 12147])).
% 2.86/3.09 tff(12149,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[2, 12148])).
% 2.86/3.09 tff(12150,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(z)), s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(12151,plain,
% 2.86/3.09 (~(s(s(z)) = elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12150, 2, 676])).
% 2.86/3.09 tff(12152,plain,
% 2.86/3.09 (b(elem!1, z)),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[3133, 4064])).
% 2.86/3.09 tff(12153,plain,
% 2.86/3.09 ($false),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[4070, 12152])).
% 2.86/3.09 tff(12154,plain,((~(elem!1 = s(z))) | b(elem!1, z) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.09 tff(12155,plain,
% 2.86/3.09 (~(elem!1 = s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12154, 4070, 12144])).
% 2.86/3.09 tff(12156,plain,
% 2.86/3.09 (b(elem!1, s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[687, 12155, 676])).
% 2.86/3.09 tff(12157,plain,
% 2.86/3.09 (r(s(s(s(z))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1173, 1168])).
% 2.86/3.09 tff(12158,plain,
% 2.86/3.09 (~(s(z) = elem!1)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1439, 12155])).
% 2.86/3.09 tff(12159,plain,
% 2.86/3.09 (~(elem!1 = s(s(z)))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3737, 12151])).
% 2.86/3.09 tff(12160,plain,
% 2.86/3.09 (~r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[9352, 554, 747, 2])).
% 2.86/3.09 tff(12161,plain,
% 2.86/3.09 (b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[479, 12160])).
% 2.86/3.09 tff(12162,plain,
% 2.86/3.09 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3777, 12161, 1421, 679])).
% 2.86/3.09 tff(12163,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12164,plain,
% 2.86/3.09 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12165,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12164])).
% 2.86/3.09 tff(12166,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[12165, 12163])).
% 2.86/3.09 tff(12167,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12168,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12167, 12166])).
% 2.86/3.09 tff(12169,plain,
% 2.86/3.09 (~b(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12168, 171, 679, 3281, 1421, 12161])).
% 2.86/3.09 tff(12170,plain,
% 2.86/3.09 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[496, 25, 12169])).
% 2.86/3.09 tff(12171,plain,
% 2.86/3.09 (r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12170, 6021])).
% 2.86/3.09 tff(12172,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12173,plain,
% 2.86/3.09 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12174,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12173])).
% 2.86/3.09 tff(12175,plain,
% 2.86/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.09 inference(transitivity,[status(thm)],[12174, 12172])).
% 2.86/3.09 tff(12176,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12177,plain,
% 2.86/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12176, 12175])).
% 2.86/3.09 tff(12178,plain,
% 2.86/3.09 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12177, 171, 679, 3281, 1421, 12161])).
% 2.86/3.09 tff(12179,plain,
% 2.86/3.09 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[143, 25, 140, 12178])).
% 2.86/3.09 tff(12180,plain,
% 2.86/3.09 ((s(s(s(s(s(z))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.86/3.09 inference(symmetry,[status(thm)],[6662])).
% 2.86/3.09 tff(12181,plain,
% 2.86/3.09 ((~(s(s(s(s(s(z))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(z)))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12180])).
% 2.86/3.09 tff(12182,plain,
% 2.86/3.09 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[3829, 12181])).
% 2.86/3.09 tff(12183,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12184,plain,
% 2.86/3.09 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12185,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12184])).
% 2.86/3.09 tff(12186,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[12185, 12183])).
% 2.86/3.09 tff(12187,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12188,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12187, 12186])).
% 2.86/3.09 tff(12189,plain,
% 2.86/3.09 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12188, 106, 4369, 12179, 12171])).
% 2.86/3.09 tff(12190,plain,
% 2.86/3.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12191,plain,
% 2.86/3.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12192,plain,
% 2.86/3.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z)))))) | r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12191, 12190])).
% 2.86/3.09 tff(12193,plain,
% 2.86/3.09 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12192, 25, 12189])).
% 2.86/3.09 tff(12194,plain,
% 2.86/3.09 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12193, 12182])).
% 2.86/3.09 tff(12195,plain,
% 2.86/3.09 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[3777, 4, 1421, 679])).
% 2.86/3.09 tff(12196,plain,
% 2.86/3.09 (~b(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12168, 171, 679, 3281, 1421, 4])).
% 2.86/3.09 tff(12197,plain,
% 2.86/3.09 ((z = s(s(s(s(s(z)))))) | r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[496, 25, 12196])).
% 2.86/3.09 tff(12198,plain,
% 2.86/3.09 (r(z, s(s(s(s(s(z))))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12197, 6021])).
% 2.86/3.09 tff(12199,plain,
% 2.86/3.09 (~b(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12177, 171, 679, 3281, 1421, 4])).
% 2.86/3.09 tff(12200,plain,
% 2.86/3.09 (r(s(s(s(s(s(z))))), z)),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[143, 25, 140, 12199])).
% 2.86/3.09 tff(12201,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12202,plain,
% 2.86/3.09 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.86/3.09 inference(rewrite,[status(thm)],[])).
% 2.86/3.09 tff(12203,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))))),
% 2.86/3.09 inference(monotonicity,[status(thm)],[12202])).
% 2.86/3.09 tff(12204,plain,
% 2.86/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.86/3.09 inference(transitivity,[status(thm)],[12203, 12201])).
% 2.86/3.09 tff(12205,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))))),
% 2.86/3.09 inference(quant_inst,[status(thm)],[])).
% 2.86/3.09 tff(12206,plain,
% 2.86/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(elem!1)))))),
% 2.86/3.09 inference(modus_ponens,[status(thm)],[12205, 12204])).
% 2.86/3.09 tff(12207,plain,
% 2.86/3.09 (~r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[12206, 106, 3035, 12200, 12198])).
% 2.86/3.09 tff(12208,plain,
% 2.86/3.09 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.86/3.09 inference(unit_resolution,[status(thm)],[1305, 12207, 1300])).
% 2.86/3.09 tff(12209,plain,
% 2.86/3.09 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.86/3.10 inference(monotonicity,[status(thm)],[693])).
% 2.86/3.10 tff(12210,plain,
% 2.86/3.10 (r(s(s(z)), z)),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[1403, 12209])).
% 2.86/3.10 tff(12211,plain,
% 2.86/3.10 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[10395, 106, 12210, 127, 1288])).
% 2.86/3.10 tff(12212,plain,
% 2.86/3.10 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[2010, 1210])).
% 2.86/3.10 tff(12213,plain,
% 2.86/3.10 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[9350, 171, 2705, 12212, 2740])).
% 2.86/3.10 tff(12214,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[225, 12213, 12211])).
% 2.86/3.10 tff(12215,plain,((~(elem!1 = z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1))))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(12216,plain,
% 2.86/3.10 (~(elem!1 = z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12215, 12200, 2740, 2705, 12198, 12208, 1403])).
% 2.86/3.10 tff(12217,plain,
% 2.86/3.10 (r(elem!1, z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1567, 12216, 4070])).
% 2.86/3.10 tff(12218,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12219,plain,
% 2.86/3.10 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12220,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12219])).
% 2.86/3.10 tff(12221,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[12220, 12218])).
% 2.86/3.10 tff(12222,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(12223,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[12222, 12221])).
% 2.86/3.10 tff(12224,plain,
% 2.86/3.10 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12223, 106, 12217, 12200, 12198])).
% 2.86/3.10 tff(12225,plain,
% 2.86/3.10 (elem!1 = s(s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[782, 12224, 12195])).
% 2.86/3.10 tff(12226,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12225])).
% 2.86/3.10 tff(12227,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.86/3.10 inference(symmetry,[status(thm)],[12226])).
% 2.86/3.10 tff(12228,plain,
% 2.86/3.10 (~(s(s(s(elem!1))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[1300, 12181])).
% 2.86/3.10 tff(12229,plain,
% 2.86/3.10 (~r(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12188, 106, 3035, 12200, 12198])).
% 2.86/3.10 tff(12230,plain,
% 2.86/3.10 ((s(s(s(elem!1))) = s(s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12192, 25, 12229])).
% 2.86/3.10 tff(12231,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12230, 12228])).
% 2.86/3.10 tff(12232,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), elem!1)),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[12231, 12227])).
% 2.86/3.10 tff(12233,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[5099, 12232])).
% 2.86/3.10 tff(12234,plain,((~b(s(s(s(s(s(z))))), s(z))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, z) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(12235,plain,
% 2.86/3.10 (~r(s(s(z)), elem!1)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12234, 12161, 4070, 9329, 9344, 5099, 3829, 4369, 679, 3281, 1421])).
% 2.86/3.10 tff(12236,plain,
% 2.86/3.10 (b(s(s(z)), elem!1)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1416, 12235, 2116])).
% 2.86/3.10 tff(12237,plain,
% 2.86/3.10 (b(s(s(z)), z)),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[666, 731])).
% 2.86/3.10 tff(12238,plain,
% 2.86/3.10 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[995, 704, 9343])).
% 2.86/3.10 tff(12239,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1013, 12238])).
% 2.86/3.10 tff(12240,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.86/3.10 tff(12241,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12242,plain,
% 2.86/3.10 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(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(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12243,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12242])).
% 2.86/3.10 tff(12244,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[12243, 12241])).
% 2.86/3.10 tff(12245,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(12246,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[12245, 12244])).
% 2.86/3.10 tff(12247,plain,
% 2.86/3.10 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12246, 171, 1421, 666, 12161, 12240])).
% 2.86/3.10 tff(12248,plain,
% 2.86/3.10 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12247, 12239])).
% 2.86/3.10 tff(12249,plain,
% 2.86/3.10 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[203, 25, 12248, 198])).
% 2.86/3.10 tff(12250,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12251,plain,
% 2.86/3.10 (((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12252,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12251])).
% 2.86/3.10 tff(12253,plain,
% 2.86/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[12252, 12250])).
% 2.86/3.10 tff(12254,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(z)))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(12255,plain,
% 2.86/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[12254, 12253])).
% 2.86/3.10 tff(12256,plain,
% 2.86/3.10 (~r(z, s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12255, 106, 127, 1288, 12249])).
% 2.86/3.10 tff(12257,plain,
% 2.86/3.10 (b(z, s(s(z)))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[124, 12256])).
% 2.86/3.10 tff(12258,plain,
% 2.86/3.10 (~r(s(s(s(s(z)))), s(z))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[11405, 12257, 12237, 821, 554, 2, 747])).
% 2.86/3.10 tff(12259,plain,
% 2.86/3.10 (b(s(s(s(s(z)))), s(z))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[321, 12258, 729])).
% 2.86/3.10 tff(12260,plain,
% 2.86/3.10 (~b(s(s(s(s(z)))), z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[9616, 171, 3281, 12144, 12259])).
% 2.86/3.10 tff(12261,plain,
% 2.86/3.10 (r(s(s(s(s(z)))), z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[272, 25, 52, 12260])).
% 2.86/3.10 tff(12262,plain,
% 2.86/3.10 (r(s(elem!1), z) <=> r(s(z), z)),
% 2.86/3.10 inference(monotonicity,[status(thm)],[710])).
% 2.86/3.10 tff(12263,plain,
% 2.86/3.10 (r(s(z), z) <=> r(s(elem!1), z)),
% 2.86/3.10 inference(symmetry,[status(thm)],[12262])).
% 2.86/3.10 tff(12264,plain,
% 2.86/3.10 ((~r(s(z), z)) <=> (~r(s(elem!1), z))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12263])).
% 2.86/3.10 tff(12265,plain,
% 2.86/3.10 (~r(s(elem!1), z)),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[6, 12264])).
% 2.86/3.10 tff(12266,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1810, 12265])).
% 2.86/3.10 tff(12267,plain,((~(s(elem!1) = s(z))) | (~r(s(elem!1), z)) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(12268,plain,
% 2.86/3.10 (~r(s(elem!1), z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12267, 704, 6])).
% 2.86/3.10 tff(12269,plain,
% 2.86/3.10 (b(s(elem!1), z)),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1691, 12268])).
% 2.86/3.10 tff(12270,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.86/3.10 inference(monotonicity,[status(thm)],[1605])).
% 2.86/3.10 tff(12271,plain,
% 2.86/3.10 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.86/3.10 inference(symmetry,[status(thm)],[12270])).
% 2.86/3.10 tff(12272,plain,
% 2.86/3.10 (b(s(s(s(elem!1))), z)),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[1847, 12271])).
% 2.86/3.10 tff(12273,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[3045, 12272])).
% 2.86/3.10 tff(12274,plain,((~(s(s(s(elem!1))) = s(elem!1))) | b(s(s(s(elem!1))), z) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(12275,plain,
% 2.86/3.10 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12274, 12269, 3045])).
% 2.86/3.10 tff(12276,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.86/3.10 tff(12277,plain,
% 2.86/3.10 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[12276])).
% 2.86/3.10 tff(12278,plain,
% 2.86/3.10 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12277])).
% 2.86/3.10 tff(12279,plain,
% 2.86/3.10 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.86/3.10 inference(transitivity,[status(thm)],[813, 12278, 720])).
% 2.86/3.10 tff(12280,plain,
% 2.86/3.10 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12279])).
% 2.86/3.10 tff(12281,plain,
% 2.86/3.10 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 2.86/3.10 inference(symmetry,[status(thm)],[12280])).
% 2.86/3.10 tff(12282,plain,
% 2.86/3.10 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(elem!1))))),
% 2.86/3.10 inference(symmetry,[status(thm)],[12278])).
% 2.86/3.10 tff(12283,plain,
% 2.86/3.10 (s(s(s(elem!1))) = s(elem!1)),
% 2.86/3.10 inference(transitivity,[status(thm)],[721, 12282, 12281, 1002])).
% 2.86/3.10 tff(12284,plain,
% 2.86/3.10 ($false),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1618, 12283])).
% 2.86/3.10 tff(12285,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.10 tff(12286,plain,
% 2.86/3.10 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12285, 12275])).
% 2.86/3.10 tff(12287,plain,
% 2.86/3.10 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[1135, 12286, 704])).
% 2.86/3.10 tff(12288,plain,
% 2.86/3.10 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[421, 12287])).
% 2.86/3.10 tff(12289,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12290,plain,
% 2.86/3.10 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12291,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.86/3.10 inference(monotonicity,[status(thm)],[12290])).
% 2.86/3.10 tff(12292,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.86/3.10 inference(transitivity,[status(thm)],[12291, 12289])).
% 2.86/3.10 tff(12293,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.86/3.10 inference(quant_inst,[status(thm)],[])).
% 2.86/3.10 tff(12294,plain,
% 2.86/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.86/3.10 inference(modus_ponens,[status(thm)],[12293, 12292])).
% 2.86/3.10 tff(12295,plain,
% 2.86/3.10 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[12294, 171, 3281, 12144, 12161, 12259])).
% 2.86/3.10 tff(12296,plain,
% 2.86/3.10 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.10 inference(unit_resolution,[status(thm)],[426, 12295, 12288])).
% 2.86/3.10 tff(12297,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12298,plain,
% 2.86/3.10 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.10 inference(rewrite,[status(thm)],[])).
% 2.86/3.10 tff(12299,plain,
% 2.86/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12298])).
% 2.86/3.11 tff(12300,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12299, 12297])).
% 2.86/3.11 tff(12301,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12302,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12301, 12300])).
% 2.86/3.11 tff(12303,plain,
% 2.86/3.11 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12302, 171, 3281, 12144, 12161, 12259])).
% 2.86/3.11 tff(12304,plain,
% 2.86/3.11 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1156, 12303, 12287])).
% 2.86/3.11 tff(12305,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[8712, 106, 12304, 12296, 1288, 12261])).
% 2.86/3.11 tff(12306,plain,((~(elem!1 = z)) | (~r(z, s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(z))))))) | b(s(s(s(elem!1))), z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12307,plain,
% 2.86/3.11 (~(elem!1 = z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12306, 12171, 3281, 554, 2, 747, 12179, 12236, 1421, 12194, 3045, 6])).
% 2.86/3.11 tff(12308,plain,
% 2.86/3.11 (r(elem!1, z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1567, 12307, 4070])).
% 2.86/3.11 tff(12309,plain,
% 2.86/3.11 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12223, 106, 12308, 12179, 12171])).
% 2.86/3.11 tff(12310,plain,
% 2.86/3.11 (elem!1 = s(s(s(s(s(z)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[782, 12309, 12162])).
% 2.86/3.11 tff(12311,plain,
% 2.86/3.11 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(s(s(s(z))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12310])).
% 2.86/3.11 tff(12312,plain,
% 2.86/3.11 (b(s(s(s(elem!1))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), elem!1)),
% 2.86/3.11 inference(symmetry,[status(thm)],[12311])).
% 2.86/3.11 tff(12313,plain,
% 2.86/3.11 (b(s(s(s(elem!1))), elem!1)),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12194, 12312])).
% 2.86/3.11 tff(12314,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[5099, 12313])).
% 2.86/3.11 tff(12315,plain,((~r(s(z), s(s(z)))) | b(s(s(s(elem!1))), elem!1) | b(elem!1, z) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), elem!1)) | b(s(s(s(elem!1))), z) | r(s(z), z) | (~b(elem!1, s(z))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12316,plain,
% 2.86/3.11 (~r(s(z), s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12315, 1421, 4070, 3281, 2, 747, 5099, 3045, 6, 12156, 12151])).
% 2.86/3.11 tff(12317,plain,
% 2.86/3.11 (b(s(z), s(s(z)))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[550, 12316])).
% 2.86/3.11 tff(12318,plain,
% 2.86/3.11 (~b(s(s(z)), elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[4888, 12317, 12156, 1421])).
% 2.86/3.11 tff(12319,plain,
% 2.86/3.11 (r(s(s(z)), elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1416, 12318, 12151])).
% 2.86/3.11 tff(12320,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12321,plain,
% 2.86/3.11 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12322,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12321])).
% 2.86/3.11 tff(12323,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12322, 12320])).
% 2.86/3.11 tff(12324,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12325,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12324, 12323])).
% 2.86/3.11 tff(12326,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12325, 171, 3137, 679, 3281, 3133])).
% 2.86/3.11 tff(12327,plain,((~b(z, s(z))) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12328,plain,
% 2.86/3.11 (~b(z, elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12327, 12156, 3281, 12144])).
% 2.86/3.11 tff(12329,plain,
% 2.86/3.11 (~b(s(s(z)), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[10236, 12317, 12144, 3281])).
% 2.86/3.11 tff(12330,plain,
% 2.86/3.11 (r(s(s(z)), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[157, 12329])).
% 2.86/3.11 tff(12331,plain,
% 2.86/3.11 (~(elem!1 = s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[7323, 3281, 258])).
% 2.86/3.11 tff(12332,plain,
% 2.86/3.11 (b(elem!1, s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[687, 12331, 676])).
% 2.86/3.11 tff(12333,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12334,plain,
% 2.86/3.11 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12335,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12334])).
% 2.86/3.11 tff(12336,plain,
% 2.86/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12335, 12333])).
% 2.86/3.11 tff(12337,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12338,plain,
% 2.86/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12337, 12336])).
% 2.86/3.11 tff(12339,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12338, 171, 1596, 12332, 3281, 3133])).
% 2.86/3.11 tff(12340,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(s(z), z)) | r(elem!1, s(z)) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12341,plain,
% 2.86/3.11 (~b(elem!1, z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12340, 258, 3133, 676, 3281])).
% 2.86/3.11 tff(12342,plain,
% 2.86/3.11 (r(z, elem!1)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[651, 258, 695])).
% 2.86/3.11 tff(12343,plain,
% 2.86/3.11 (~r(elem!1, z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[7533, 12342, 637, 1403])).
% 2.86/3.11 tff(12344,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1567, 12343, 12341, 3218])).
% 2.86/3.11 tff(12345,plain,(b(z, elem!1) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)) | (~b(s(z), z)) | r(elem!1, s(z)) | (~b(z, s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12346,plain,
% 2.86/3.11 (z = elem!1),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12345, 12330, 676, 12144, 12328, 3281, 12319])).
% 2.86/3.11 tff(12347,plain,
% 2.86/3.11 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12346])).
% 2.86/3.11 tff(12348,plain,
% 2.86/3.11 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12347, 759])).
% 2.86/3.11 tff(12349,plain,
% 2.86/3.11 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12348])).
% 2.86/3.11 tff(12350,plain,
% 2.86/3.11 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[140, 12349])).
% 2.86/3.11 tff(12351,plain,
% 2.86/3.11 (s(elem!1) = s(z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[703, 12346])).
% 2.86/3.11 tff(12352,plain,
% 2.86/3.11 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[3828, 12151])).
% 2.86/3.11 tff(12353,plain,
% 2.86/3.11 (~r(s(elem!1), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12267, 12351, 6])).
% 2.86/3.11 tff(12354,plain,
% 2.86/3.11 (b(s(elem!1), z)),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1691, 12353])).
% 2.86/3.11 tff(12355,plain,
% 2.86/3.11 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12274, 12354, 3045])).
% 2.86/3.11 tff(12356,plain,
% 2.86/3.11 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12285, 12355])).
% 2.86/3.11 tff(12357,plain,
% 2.86/3.11 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1135, 12356, 12351])).
% 2.86/3.11 tff(12358,plain,
% 2.86/3.11 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[1082, 4775])).
% 2.86/3.11 tff(12359,plain,
% 2.86/3.11 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12358, 10781])).
% 2.86/3.11 tff(12360,plain,
% 2.86/3.11 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.86/3.11 inference(monotonicity,[status(thm)],[4355])).
% 2.86/3.11 tff(12361,plain,
% 2.86/3.11 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.86/3.11 inference(symmetry,[status(thm)],[12360])).
% 2.86/3.11 tff(12362,plain,
% 2.86/3.11 (r(s(s(elem!1)), elem!1)),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[1403, 12361])).
% 2.86/3.11 tff(12363,plain,
% 2.86/3.11 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[4355])).
% 2.86/3.11 tff(12364,plain,
% 2.86/3.11 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.11 inference(symmetry,[status(thm)],[12363])).
% 2.86/3.11 tff(12365,plain,
% 2.86/3.11 (r(s(s(s(z))), s(s(elem!1)))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[1199, 12364])).
% 2.86/3.11 tff(12366,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12367,plain,
% 2.86/3.11 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12368,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12367])).
% 2.86/3.11 tff(12369,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12368, 12366])).
% 2.86/3.11 tff(12370,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12371,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12370, 12369])).
% 2.86/3.11 tff(12372,plain,
% 2.86/3.11 ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12371, 106])).
% 2.86/3.11 tff(12373,plain,
% 2.86/3.11 (~r(elem!1, s(s(s(z))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12372, 12365, 2049, 12362])).
% 2.86/3.11 tff(12374,plain,
% 2.86/3.11 (b(elem!1, s(s(s(elem!1))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[942, 12373, 1930])).
% 2.86/3.11 tff(12375,plain,
% 2.86/3.11 (b(elem!1, s(s(s(z))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[948, 12374, 1930])).
% 2.86/3.11 tff(12376,plain,
% 2.86/3.11 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[4356])).
% 2.86/3.11 tff(12377,plain,
% 2.86/3.11 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12376])).
% 2.86/3.11 tff(12378,plain,
% 2.86/3.11 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.86/3.11 inference(monotonicity,[status(thm)],[672])).
% 2.86/3.11 tff(12379,plain,
% 2.86/3.11 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12378, 1043])).
% 2.86/3.11 tff(12380,plain,
% 2.86/3.11 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12379])).
% 2.86/3.11 tff(12381,plain,
% 2.86/3.11 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[1050, 12380])).
% 2.86/3.11 tff(12382,plain,
% 2.86/3.11 (r(elem!1, s(s(s(s(elem!1))))) <=> r(z, s(s(s(s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[784, 12376])).
% 2.86/3.11 tff(12383,plain,
% 2.86/3.11 (r(z, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(symmetry,[status(thm)],[12382])).
% 2.86/3.11 tff(12384,plain,
% 2.86/3.11 (r(elem!1, s(s(s(s(z))))) <=> r(z, s(s(s(s(z)))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[784])).
% 2.86/3.11 tff(12385,plain,
% 2.86/3.11 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12384, 12383])).
% 2.86/3.11 tff(12386,plain,
% 2.86/3.11 ((~r(elem!1, s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(elem!1))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12385])).
% 2.86/3.11 tff(12387,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12388,plain,
% 2.86/3.11 (((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12389,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12388])).
% 2.86/3.11 tff(12390,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12389, 12387])).
% 2.86/3.11 tff(12391,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12392,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12391, 12390])).
% 2.86/3.11 tff(12393,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12392, 106, 1403, 2049, 1199, 2448])).
% 2.86/3.11 tff(12394,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12395,plain,
% 2.86/3.11 (~r(elem!1, s(s(s(s(z)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12394, 1199, 2049, 1403])).
% 2.86/3.11 tff(12396,plain,
% 2.86/3.11 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12395, 12386])).
% 2.86/3.11 tff(12397,plain,
% 2.86/3.11 (((~![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))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12398,plain,
% 2.86/3.11 ((~![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))))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12399,plain,
% 2.86/3.11 ((~![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)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12398, 12397])).
% 2.86/3.11 tff(12400,plain,
% 2.86/3.11 ((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)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12399, 25])).
% 2.86/3.11 tff(12401,plain,
% 2.86/3.11 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12400, 12396, 12381])).
% 2.86/3.11 tff(12402,plain,
% 2.86/3.11 (b(elem!1, s(s(s(s(z)))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12401, 12377])).
% 2.86/3.11 tff(12403,plain,
% 2.86/3.11 (~(s(s(s(s(z)))) = s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[728, 1930])).
% 2.86/3.11 tff(12404,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12405,plain,
% 2.86/3.11 (((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(rewrite,[status(thm)],[])).
% 2.86/3.11 tff(12406,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(elem!1, s(s(s(s(s(z)))))))))),
% 2.86/3.11 inference(monotonicity,[status(thm)],[12405])).
% 2.86/3.11 tff(12407,plain,
% 2.86/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.86/3.11 inference(transitivity,[status(thm)],[12406, 12404])).
% 2.86/3.11 tff(12408,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.11 inference(quant_inst,[status(thm)],[])).
% 2.86/3.11 tff(12409,plain,
% 2.86/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(s(s(z)))))))),
% 2.86/3.11 inference(modus_ponens,[status(thm)],[12408, 12407])).
% 2.86/3.11 tff(12410,plain,
% 2.86/3.11 ($false),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12409, 106, 1403, 2049, 769, 1199])).
% 2.86/3.11 tff(12411,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.11 tff(12412,plain,
% 2.86/3.11 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[12411, 1199, 2049, 1403])).
% 2.86/3.11 tff(12413,plain,
% 2.86/3.11 (b(elem!1, s(s(s(s(s(z))))))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[782, 12412, 1895])).
% 2.86/3.11 tff(12414,plain,
% 2.86/3.11 (~b(s(s(s(s(s(z))))), s(z))),
% 2.86/3.11 inference(unit_resolution,[status(thm)],[3777, 12413, 1421, 679])).
% 2.86/3.11 tff(12415,plain,
% 2.86/3.11 (r(s(s(s(s(s(z))))), s(z))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[479, 12414])).
% 2.86/3.12 tff(12416,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12417,plain,
% 2.86/3.12 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12418,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[12417])).
% 2.86/3.12 tff(12419,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.86/3.12 inference(transitivity,[status(thm)],[12418, 12416])).
% 2.86/3.12 tff(12420,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(12421,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[12420, 12419])).
% 2.86/3.12 tff(12422,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12421, 106, 2, 2463, 2049, 1199])).
% 2.86/3.12 tff(12423,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(12424,plain,
% 2.86/3.12 (~r(elem!1, s(s(z)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12423, 1199, 2049, 2])).
% 2.86/3.12 tff(12425,plain,
% 2.86/3.12 (b(elem!1, s(s(z)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[3154, 12424, 3122])).
% 2.86/3.12 tff(12426,plain,
% 2.86/3.12 (~(s(s(z)) = s(s(s(s(z)))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[4725, 10778])).
% 2.86/3.12 tff(12427,assumption,(r(s(s(elem!1)), s(s(s(s(s(z))))))), introduced(assumption)).
% 2.86/3.12 tff(12428,plain,
% 2.86/3.12 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[12427, 4720])).
% 2.86/3.12 tff(12429,plain,
% 2.86/3.12 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[508, 106, 260, 502])).
% 2.86/3.12 tff(12430,plain,
% 2.86/3.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12429, 12428])).
% 2.86/3.12 tff(12431,plain,
% 2.86/3.12 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[349, 25, 12430])).
% 2.86/3.12 tff(12432,plain,
% 2.86/3.12 (b(s(s(z)), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12431, 12426])).
% 2.86/3.12 tff(12433,plain,
% 2.86/3.12 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[585, 106, 260, 502])).
% 2.86/3.12 tff(12434,plain,
% 2.86/3.12 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12433, 12428])).
% 2.86/3.12 tff(12435,plain,
% 2.86/3.12 (b(s(s(s(s(z)))), s(s(z)))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[372, 25, 4725, 12434])).
% 2.86/3.12 tff(12436,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12437,plain,
% 2.86/3.12 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12438,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[12437])).
% 2.86/3.12 tff(12439,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.86/3.12 inference(transitivity,[status(thm)],[12438, 12436])).
% 2.86/3.12 tff(12440,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(12441,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[12440, 12439])).
% 2.86/3.12 tff(12442,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12441, 171, 323, 1421, 4176, 12435, 12432])).
% 2.86/3.12 tff(12443,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(12444,plain,
% 2.86/3.12 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12443, 260, 1421, 502, 323, 4176, 710])).
% 2.86/3.12 tff(12445,plain,
% 2.86/3.12 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[878, 12444, 4721])).
% 2.86/3.12 tff(12446,plain,
% 2.86/3.12 (b(s(s(elem!1)), s(s(s(s(s(z)))))) <=> b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[711])).
% 2.86/3.12 tff(12447,plain,
% 2.86/3.12 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[1273, 12446])).
% 2.86/3.12 tff(12448,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[200, 12447])).
% 2.86/3.12 tff(12449,plain,((~b(s(s(elem!1)), s(s(s(s(s(z))))))) | b(s(s(z)), s(s(s(s(s(z)))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(12450,plain,
% 2.86/3.12 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12449, 12445, 710])).
% 2.86/3.12 tff(12451,plain,
% 2.86/3.12 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[1082, 4725])).
% 2.86/3.12 tff(12452,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12453,plain,
% 2.86/3.12 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12454,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[12453])).
% 2.86/3.12 tff(12455,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.86/3.12 inference(transitivity,[status(thm)],[12454, 12452])).
% 2.86/3.12 tff(12456,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(12457,plain,
% 2.86/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[12456, 12455])).
% 2.86/3.12 tff(12458,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12457, 171, 323, 1421, 4176, 1384, 2038, 160])).
% 2.86/3.12 tff(12459,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(12460,plain,
% 2.86/3.12 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12459, 12450, 1421, 4176, 2038, 323])).
% 2.86/3.12 tff(12461,plain,
% 2.86/3.12 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[1368, 12460])).
% 2.86/3.12 tff(12462,plain,
% 2.86/3.12 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[8834, 1357, 5609, 260])).
% 2.86/3.12 tff(12463,plain,
% 2.86/3.12 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[1102, 25, 2839, 12462])).
% 2.86/3.12 tff(12464,plain,
% 2.86/3.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12092, 12463, 2433, 2038])).
% 2.86/3.12 tff(12465,plain,
% 2.86/3.12 ((s(s(s(s(z)))) = s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[4240, 25, 12464])).
% 2.86/3.12 tff(12466,plain,
% 2.86/3.12 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12465, 10782])).
% 2.86/3.12 tff(12467,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12468,plain,
% 2.86/3.12 (((~r(s(s(s(z))), elem!1)) | (~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(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.12 inference(rewrite,[status(thm)],[])).
% 2.86/3.12 tff(12469,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.86/3.12 inference(monotonicity,[status(thm)],[12468])).
% 2.86/3.12 tff(12470,plain,
% 2.86/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.86/3.12 inference(transitivity,[status(thm)],[12469, 12467])).
% 2.86/3.12 tff(12471,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~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))))))))),
% 2.86/3.12 inference(quant_inst,[status(thm)],[])).
% 2.86/3.12 tff(12472,plain,
% 2.86/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.86/3.12 inference(modus_ponens,[status(thm)],[12471, 12470])).
% 2.86/3.12 tff(12473,plain,
% 2.86/3.12 ($false),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12472, 106, 260, 2049, 1357, 12466])).
% 2.86/3.12 tff(12474,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.86/3.12 tff(12475,plain,
% 2.86/3.12 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[12474, 12461, 2049, 12451, 2433, 2038, 260])).
% 2.86/3.12 tff(12476,plain,
% 2.86/3.12 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.86/3.12 inference(unit_resolution,[status(thm)],[426, 12475, 10875])).
% 2.86/3.12 tff(12477,plain,
% 2.86/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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)))))))),
% 2.96/3.12 inference(rewrite,[status(thm)],[])).
% 2.96/3.12 tff(12478,plain,
% 2.96/3.12 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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)))))))),
% 2.96/3.12 inference(rewrite,[status(thm)],[])).
% 2.96/3.12 tff(12479,plain,
% 2.96/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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))))))))),
% 2.96/3.12 inference(monotonicity,[status(thm)],[12478])).
% 2.96/3.12 tff(12480,plain,
% 2.96/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, 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)))))))),
% 2.96/3.12 inference(transitivity,[status(thm)],[12479, 12477])).
% 2.96/3.12 tff(12481,plain,
% 2.96/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)))),
% 2.96/3.12 inference(quant_inst,[status(thm)],[])).
% 2.96/3.12 tff(12482,plain,
% 2.96/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.96/3.12 inference(modus_ponens,[status(thm)],[12481, 12480])).
% 2.96/3.12 tff(12483,plain,
% 2.96/3.12 ($false),
% 2.96/3.12 inference(unit_resolution,[status(thm)],[12482, 171, 323, 1421, 4176, 12476, 2433, 12450])).
% 2.96/3.12 tff(12484,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(s(s(z))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.12 tff(12485,plain,
% 2.96/3.12 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.12 inference(unit_resolution,[status(thm)],[12484, 12425, 1421, 323, 12402, 1314, 2049, 12375, 1930, 12415])).
% 2.96/3.12 tff(12486,plain,
% 2.96/3.12 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.12 inference(unit_resolution,[status(thm)],[1156, 12485, 419])).
% 2.96/3.12 tff(12487,plain,
% 2.96/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12488,plain,
% 2.96/3.13 (((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12489,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 2.96/3.13 inference(monotonicity,[status(thm)],[12488])).
% 2.96/3.13 tff(12490,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(transitivity,[status(thm)],[12489, 12487])).
% 2.96/3.13 tff(12491,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12492,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 2.96/3.13 inference(modus_ponens,[status(thm)],[12491, 12490])).
% 2.96/3.13 tff(12493,plain,
% 2.96/3.13 ($false),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12492, 171, 679, 1421, 3686, 840, 2433, 357])).
% 2.96/3.13 tff(12494,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.13 tff(12495,plain,
% 2.96/3.13 (~b(s(s(s(s(z)))), s(z))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12494, 12486, 1421, 12413, 12402, 679])).
% 2.96/3.13 tff(12496,plain,
% 2.96/3.13 (r(s(s(s(s(z)))), s(z))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[321, 12495, 12403])).
% 2.96/3.13 tff(12497,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12498,plain,
% 2.96/3.13 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12499,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 2.96/3.13 inference(monotonicity,[status(thm)],[12498])).
% 2.96/3.13 tff(12500,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.96/3.13 inference(transitivity,[status(thm)],[12499, 12497])).
% 2.96/3.13 tff(12501,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12502,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.96/3.13 inference(modus_ponens,[status(thm)],[12501, 12500])).
% 2.96/3.13 tff(12503,plain,
% 2.96/3.13 ($false),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12502, 171, 3686, 83, 840, 2433])).
% 2.96/3.13 tff(12504,plain,((~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(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.13 tff(12505,plain,
% 2.96/3.13 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12504, 12486, 12413, 12402])).
% 2.96/3.13 tff(12506,plain,
% 2.96/3.13 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[426, 12505, 1314])).
% 2.96/3.13 tff(12507,plain,
% 2.96/3.13 (~r(s(z), s(s(s(s(s(z))))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[10256, 1199, 2, 747])).
% 2.96/3.13 tff(12508,plain,
% 2.96/3.13 (b(s(z), s(s(s(s(s(z))))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[60, 12507])).
% 2.96/3.13 tff(12509,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12510,plain,
% 2.96/3.13 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12511,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.96/3.13 inference(monotonicity,[status(thm)],[12510])).
% 2.96/3.13 tff(12512,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(transitivity,[status(thm)],[12511, 12509])).
% 2.96/3.13 tff(12513,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12514,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.96/3.13 inference(modus_ponens,[status(thm)],[12513, 12512])).
% 2.96/3.13 tff(12515,plain,
% 2.96/3.13 ($false),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12514, 171, 1421, 840, 1275, 1384, 2433, 2852])).
% 2.96/3.13 tff(12516,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.13 tff(12517,plain,
% 2.96/3.13 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12516, 1384, 840, 1275, 1421, 2433])).
% 2.96/3.13 tff(12518,plain,
% 2.96/3.13 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[2842, 12517, 2839])).
% 2.96/3.13 tff(12519,plain,
% 2.96/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12520,plain,
% 2.96/3.13 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12521,plain,
% 2.96/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.96/3.13 inference(monotonicity,[status(thm)],[12520])).
% 2.96/3.13 tff(12522,plain,
% 2.96/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(transitivity,[status(thm)],[12521, 12519])).
% 2.96/3.13 tff(12523,plain,
% 2.96/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(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))))))))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12524,plain,
% 2.96/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.96/3.13 inference(modus_ponens,[status(thm)],[12523, 12522])).
% 2.96/3.13 tff(12525,plain,
% 2.96/3.13 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12524, 106, 5609, 263, 12518])).
% 2.96/3.13 tff(12526,plain,
% 2.96/3.13 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[2614, 12525])).
% 2.96/3.13 tff(12527,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12528,plain,
% 2.96/3.13 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12529,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.96/3.13 inference(monotonicity,[status(thm)],[12528])).
% 2.96/3.13 tff(12530,plain,
% 2.96/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(transitivity,[status(thm)],[12529, 12527])).
% 2.96/3.13 tff(12531,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12532,plain,
% 2.96/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.96/3.13 inference(modus_ponens,[status(thm)],[12531, 12530])).
% 2.96/3.13 tff(12533,plain,
% 2.96/3.13 ($false),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12532, 171, 840, 12526, 1384, 2038])).
% 2.96/3.13 tff(12534,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.13 tff(12535,plain,
% 2.96/3.13 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12534, 12413, 12375, 12506, 12496, 12358, 12508, 1421, 12402])).
% 2.96/3.13 tff(12536,plain,
% 2.96/3.13 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[1368, 12535])).
% 2.96/3.13 tff(12537,plain,
% 2.96/3.13 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12068, 12536, 12506, 12496])).
% 2.96/3.13 tff(12538,plain,
% 2.96/3.13 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[2842, 12537, 12358])).
% 2.96/3.13 tff(12539,plain,
% 2.96/3.13 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12092, 12538, 12402, 12375])).
% 2.96/3.13 tff(12540,plain,
% 2.96/3.13 ((s(s(s(s(z)))) = s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[4240, 25, 12539])).
% 2.96/3.13 tff(12541,plain,
% 2.96/3.13 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.96/3.13 inference(unit_resolution,[status(thm)],[12540, 12359])).
% 2.96/3.13 tff(12542,plain,
% 2.96/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.96/3.13 inference(rewrite,[status(thm)],[])).
% 2.96/3.13 tff(12543,plain,
% 2.96/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.96/3.13 inference(quant_inst,[status(thm)],[])).
% 2.96/3.13 tff(12544,plain,
% 2.96/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12543, 12542])).
% 2.96/3.14 tff(12545,plain,
% 2.96/3.14 ($false),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12544, 106, 2049, 12506, 12536, 12541])).
% 2.96/3.14 tff(12546,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~(z = elem!1)) | (~r(s(s(z)), elem!1)) | (elem!1 = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.14 tff(12547,plain,
% 2.96/3.14 (~r(s(s(s(z))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12546, 1421, 2049, 12156, 12357, 12317, 12346, 12319, 12159, 2, 747])).
% 2.96/3.14 tff(12548,plain,
% 2.96/3.14 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[995, 12547, 12351])).
% 2.96/3.14 tff(12549,plain,
% 2.96/3.14 (b(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[1013, 12548])).
% 2.96/3.14 tff(12550,plain,
% 2.96/3.14 (b(s(s(s(z))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[1020, 12549, 12351])).
% 2.96/3.14 tff(12551,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12552,plain,
% 2.96/3.14 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12553,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 2.96/3.14 inference(monotonicity,[status(thm)],[12552])).
% 2.96/3.14 tff(12554,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 2.96/3.14 inference(transitivity,[status(thm)],[12553, 12551])).
% 2.96/3.14 tff(12555,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12556,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12555, 12554])).
% 2.96/3.14 tff(12557,plain,
% 2.96/3.14 (~b(s(z), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12556, 171, 323, 2705, 2740])).
% 2.96/3.14 tff(12558,plain,
% 2.96/3.14 (r(s(z), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[1996, 12557])).
% 2.96/3.14 tff(12559,plain,
% 2.96/3.14 (~b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12234, 2740, 4070, 1403, 2705, 5099, 1300, 3035, 679, 3281, 1421])).
% 2.96/3.14 tff(12560,plain,
% 2.96/3.14 (r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[479, 12559])).
% 2.96/3.14 tff(12561,plain,
% 2.96/3.14 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[10963, 106, 2, 12560, 12558])).
% 2.96/3.14 tff(12562,plain,
% 2.96/3.14 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[203, 25, 12561, 198])).
% 2.96/3.14 tff(12563,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12564,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12565,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12564, 12563])).
% 2.96/3.14 tff(12566,plain,
% 2.96/3.14 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12565, 106, 12560, 12558, 747])).
% 2.96/3.14 tff(12567,plain,
% 2.96/3.14 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[1368, 12566])).
% 2.96/3.14 tff(12568,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12569,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12570,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12569, 12568])).
% 2.96/3.14 tff(12571,plain,
% 2.96/3.14 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12570, 106, 12560, 12558, 747])).
% 2.96/3.14 tff(12572,plain,
% 2.96/3.14 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[2614, 12571])).
% 2.96/3.14 tff(12573,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12574,plain,
% 2.96/3.14 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(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(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12575,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.96/3.14 inference(monotonicity,[status(thm)],[12574])).
% 2.96/3.14 tff(12576,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(transitivity,[status(thm)],[12575, 12573])).
% 2.96/3.14 tff(12577,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12578,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12577, 12576])).
% 2.96/3.14 tff(12579,plain,
% 2.96/3.14 ($false),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12578, 171, 12572, 12567, 12562, 2740])).
% 2.96/3.14 tff(12580,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | b(elem!1, z) | (~r(s(s(z)), elem!1)) | b(s(s(s(elem!1))), elem!1) | (s(s(s(s(s(z))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.14 tff(12581,plain,
% 2.96/3.14 (~b(s(s(z)), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12580, 12317, 2, 747, 12550, 4070, 12319, 5099, 12352, 4369, 12156, 3281, 1421])).
% 2.96/3.14 tff(12582,plain,
% 2.96/3.14 ((s(s(z)) = s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[979, 25, 12581])).
% 2.96/3.14 tff(12583,plain,
% 2.96/3.14 (r(s(s(z)), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12582, 900])).
% 2.96/3.14 tff(12584,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12585,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12586,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12585, 12584])).
% 2.96/3.14 tff(12587,plain,
% 2.96/3.14 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12586, 106, 2049, 1357, 2678])).
% 2.96/3.14 tff(12588,plain,
% 2.96/3.14 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[225, 12587])).
% 2.96/3.14 tff(12589,plain,
% 2.96/3.14 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.96/3.14 inference(monotonicity,[status(thm)],[1270])).
% 2.96/3.14 tff(12590,plain,
% 2.96/3.14 (r(s(s(elem!1)), s(s(s(z))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[2678, 12589])).
% 2.96/3.14 tff(12591,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12592,plain,
% 2.96/3.14 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12593,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.96/3.14 inference(monotonicity,[status(thm)],[12592])).
% 2.96/3.14 tff(12594,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.14 inference(transitivity,[status(thm)],[12593, 12591])).
% 2.96/3.14 tff(12595,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12596,plain,
% 2.96/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12595, 12594])).
% 2.96/3.14 tff(12597,plain,
% 2.96/3.14 ((~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(z))))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12596, 106])).
% 2.96/3.14 tff(12598,plain,
% 2.96/3.14 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12597, 1357, 2049, 12590])).
% 2.96/3.14 tff(12599,plain,
% 2.96/3.14 (b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[878, 12598, 4721])).
% 2.96/3.14 tff(12600,plain,
% 2.96/3.14 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12449, 12599, 710])).
% 2.96/3.14 tff(12601,plain,
% 2.96/3.14 (~b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[10418, 171, 323, 12600, 12588])).
% 2.96/3.14 tff(12602,plain,
% 2.96/3.14 (r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[479, 12601])).
% 2.96/3.14 tff(12603,plain,
% 2.96/3.14 (((~b(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))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), 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(z), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(rewrite,[status(thm)],[])).
% 2.96/3.14 tff(12604,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.96/3.14 inference(monotonicity,[status(thm)],[12603])).
% 2.96/3.14 tff(12605,plain,
% 2.96/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(transitivity,[status(thm)],[12604, 8492])).
% 2.96/3.14 tff(12606,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.14 inference(quant_inst,[status(thm)],[])).
% 2.96/3.14 tff(12607,plain,
% 2.96/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.96/3.14 inference(modus_ponens,[status(thm)],[12606, 12605])).
% 2.96/3.14 tff(12608,plain,
% 2.96/3.14 (~b(s(z), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12607, 171, 323, 12600, 12588])).
% 2.96/3.14 tff(12609,plain,
% 2.96/3.14 (r(s(z), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[60, 12608])).
% 2.96/3.14 tff(12610,plain,
% 2.96/3.14 ($false),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[10678, 106, 12609, 1357, 12602, 747])).
% 2.96/3.14 tff(12611,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.14 tff(12612,plain,
% 2.96/3.14 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[12611, 12317, 747, 2049, 12583, 12351])).
% 2.96/3.14 tff(12613,plain,
% 2.96/3.14 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[1368, 12612])).
% 2.96/3.14 tff(12614,plain,
% 2.96/3.14 (~r(s(z), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[10458, 12583, 747, 2])).
% 2.96/3.14 tff(12615,plain,
% 2.96/3.14 (b(s(z), s(s(s(s(s(z))))))),
% 2.96/3.14 inference(unit_resolution,[status(thm)],[60, 12614])).
% 2.96/3.14 tff(12616,plain,
% 2.96/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12617,plain,
% 2.96/3.15 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12618,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12617])).
% 2.96/3.15 tff(12619,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.96/3.15 inference(transitivity,[status(thm)],[12618, 12616])).
% 2.96/3.15 tff(12620,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12621,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12620, 12619])).
% 2.96/3.15 tff(12622,plain,
% 2.96/3.15 ($false),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12621, 106, 2463, 1403, 2049, 2678])).
% 2.96/3.15 tff(12623,plain,((~r(elem!1, s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.15 tff(12624,plain,
% 2.96/3.15 (~r(elem!1, s(s(z)))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12623, 12319, 2049, 12583])).
% 2.96/3.15 tff(12625,plain,
% 2.96/3.15 (b(elem!1, s(s(z)))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[3154, 12624, 12159])).
% 2.96/3.15 tff(12626,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12627,plain,
% 2.96/3.15 (((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12628,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12627])).
% 2.96/3.15 tff(12629,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(transitivity,[status(thm)],[12628, 12626])).
% 2.96/3.15 tff(12630,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), elem!1)))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12631,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12630, 12629])).
% 2.96/3.15 tff(12632,plain,
% 2.96/3.15 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12631, 171, 1421, 12625, 12550, 12615, 12613])).
% 2.96/3.15 tff(12633,plain,
% 2.96/3.15 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.96/3.15 inference(transitivity,[status(thm)],[12348, 760])).
% 2.96/3.15 tff(12634,plain,
% 2.96/3.15 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12633])).
% 2.96/3.15 tff(12635,plain,
% 2.96/3.15 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[140, 12634])).
% 2.96/3.15 tff(12636,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12637,plain,
% 2.96/3.15 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12638,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12637])).
% 2.96/3.15 tff(12639,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(transitivity,[status(thm)],[12638, 12636])).
% 2.96/3.15 tff(12640,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12641,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12640, 12639])).
% 2.96/3.15 tff(12642,plain,
% 2.96/3.15 ($false),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12641, 171, 679, 1421, 839, 1275])).
% 2.96/3.15 tff(12643,plain,((~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.15 tff(12644,plain,
% 2.96/3.15 (~b(s(s(s(s(s(z))))), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12643, 12615, 1421, 12156])).
% 2.96/3.15 tff(12645,plain,
% 2.96/3.15 (r(s(s(s(s(s(z))))), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[853, 12644, 12635])).
% 2.96/3.15 tff(12646,plain,
% 2.96/3.15 (s(s(elem!1)) = s(s(z))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12351])).
% 2.96/3.15 tff(12647,plain,
% 2.96/3.15 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12646])).
% 2.96/3.15 tff(12648,plain,
% 2.96/3.15 (~(s(s(elem!1)) = s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[745, 12351])).
% 2.96/3.15 tff(12649,plain,
% 2.96/3.15 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12646])).
% 2.96/3.15 tff(12650,plain,
% 2.96/3.15 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 2.96/3.15 inference(symmetry,[status(thm)],[12649])).
% 2.96/3.15 tff(12651,plain,
% 2.96/3.15 (r(s(s(elem!1)), elem!1)),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12319, 12650])).
% 2.96/3.15 tff(12652,plain,
% 2.96/3.15 (s(s(z)) = s(s(elem!1))),
% 2.96/3.15 inference(symmetry,[status(thm)],[12646])).
% 2.96/3.15 tff(12653,plain,
% 2.96/3.15 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12652])).
% 2.96/3.15 tff(12654,plain,
% 2.96/3.15 (r(s(s(elem!1)), s(s(s(z))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12583, 12653])).
% 2.96/3.15 tff(12655,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12656,plain,
% 2.96/3.15 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12657,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12656])).
% 2.96/3.15 tff(12658,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.96/3.15 inference(transitivity,[status(thm)],[12657, 12655])).
% 2.96/3.15 tff(12659,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12660,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12659, 12658])).
% 2.96/3.15 tff(12661,plain,
% 2.96/3.15 ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12660, 106])).
% 2.96/3.15 tff(12662,plain,
% 2.96/3.15 (~r(elem!1, s(s(s(z))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12661, 12654, 2049, 12651])).
% 2.96/3.15 tff(12663,plain,
% 2.96/3.15 (b(elem!1, s(s(s(elem!1))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[942, 12662, 12351])).
% 2.96/3.15 tff(12664,plain,
% 2.96/3.15 (b(elem!1, s(s(s(z))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[948, 12663, 12351])).
% 2.96/3.15 tff(12665,plain,
% 2.96/3.15 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12459, 12625, 1421, 12613, 12664, 12317])).
% 2.96/3.15 tff(12666,plain,
% 2.96/3.15 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12449, 12665, 12351])).
% 2.96/3.15 tff(12667,plain,
% 2.96/3.15 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[878, 12666, 12648])).
% 2.96/3.15 tff(12668,plain,
% 2.96/3.15 (r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12667, 12647])).
% 2.96/3.15 tff(12669,plain,
% 2.96/3.15 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[5017, 12668, 12645, 12319])).
% 2.96/3.15 tff(12670,plain,
% 2.96/3.15 ($false),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[782, 12669, 12632, 12350])).
% 2.96/3.15 tff(12671,plain,((~b(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | b(elem!1, z) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | b(s(s(s(elem!1))), z) | r(s(z), z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.15 tff(12672,plain,
% 2.96/3.15 (~b(s(z), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12671, 2049, 747, 2, 4070, 5099, 3281, 3045, 6, 676])).
% 2.96/3.15 tff(12673,plain,
% 2.96/3.15 (r(s(z), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[1444, 12672, 12158])).
% 2.96/3.15 tff(12674,plain,
% 2.96/3.15 (r(s(z), z)),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[1446, 1922])).
% 2.96/3.15 tff(12675,plain,
% 2.96/3.15 ($false),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[6, 12674])).
% 2.96/3.15 tff(12676,plain,((~(z = elem!1)) | r(s(z), z) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.15 tff(12677,plain,
% 2.96/3.15 (~(z = elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12676, 12673, 6])).
% 2.96/3.15 tff(12678,plain,
% 2.96/3.15 (~(elem!1 = z)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[697, 12677])).
% 2.96/3.15 tff(12679,plain,
% 2.96/3.15 (r(elem!1, z)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[1567, 12678, 4070])).
% 2.96/3.15 tff(12680,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12681,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12682,plain,
% 2.96/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z)))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12681, 12680])).
% 2.96/3.15 tff(12683,plain,
% 2.96/3.15 ($false),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12682, 106, 12679, 12673, 2049, 747])).
% 2.96/3.15 tff(12684,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(z))) | b(elem!1, z) | r(s(z), z) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), elem!1) | (~b(z, s(z))) | b(s(s(s(elem!1))), z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.15 tff(12685,plain,
% 2.96/3.15 (~r(s(s(s(z))), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12684, 12157, 4070, 6, 2, 5099, 3281, 3045, 676])).
% 2.96/3.15 tff(12686,plain,
% 2.96/3.15 (~(s(s(s(z))) = elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[2594, 1168, 679])).
% 2.96/3.15 tff(12687,plain,
% 2.96/3.15 (b(s(s(s(z))), elem!1)),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[804, 12686, 799])).
% 2.96/3.15 tff(12688,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12689,plain,
% 2.96/3.15 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.15 inference(rewrite,[status(thm)],[])).
% 2.96/3.15 tff(12690,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.96/3.15 inference(monotonicity,[status(thm)],[12689])).
% 2.96/3.15 tff(12691,plain,
% 2.96/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.15 inference(transitivity,[status(thm)],[12690, 12688])).
% 2.96/3.15 tff(12692,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 2.96/3.15 inference(quant_inst,[status(thm)],[])).
% 2.96/3.15 tff(12693,plain,
% 2.96/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.96/3.15 inference(modus_ponens,[status(thm)],[12692, 12691])).
% 2.96/3.15 tff(12694,plain,
% 2.96/3.15 (~b(elem!1, s(s(z)))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[12693, 171, 679, 666, 9344, 837])).
% 2.96/3.15 tff(12695,plain,
% 2.96/3.15 (r(elem!1, s(s(z)))),
% 2.96/3.15 inference(unit_resolution,[status(thm)],[3154, 12694, 3122])).
% 2.96/3.15 tff(12696,plain,
% 2.96/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12697,plain,
% 2.96/3.16 (((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12698,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12697])).
% 2.96/3.16 tff(12699,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12698, 12696])).
% 2.96/3.16 tff(12700,plain,
% 2.96/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(elem!1, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1)))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12701,plain,
% 2.96/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), elem!1))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12700, 12699])).
% 2.96/3.16 tff(12702,plain,
% 2.96/3.16 (~r(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12701, 106, 554, 2, 12695])).
% 2.96/3.16 tff(12703,plain,
% 2.96/3.16 (b(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1444, 12702, 1651])).
% 2.96/3.16 tff(12704,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12705,plain,
% 2.96/3.16 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12706,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12705])).
% 2.96/3.16 tff(12707,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12706, 12704])).
% 2.96/3.16 tff(12708,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12709,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12708, 12707])).
% 2.96/3.16 tff(12710,plain,
% 2.96/3.16 ($false),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12709, 171, 679, 12703, 666, 9344, 837])).
% 2.96/3.16 tff(12711,plain,((~r(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (s(z) = elem!1) | (~r(s(s(z)), s(z))) | (elem!1 = s(s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.16 tff(12712,plain,
% 2.96/3.16 (~r(s(z), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12711, 12687, 666, 679, 1651, 2, 3122, 12157])).
% 2.96/3.16 tff(12713,plain,
% 2.96/3.16 (b(s(z), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[550, 12712])).
% 2.96/3.16 tff(12714,plain,
% 2.96/3.16 (~b(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[4888, 12713, 679, 666])).
% 2.96/3.16 tff(12715,plain,
% 2.96/3.16 (r(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1444, 12714, 1651])).
% 2.96/3.16 tff(12716,plain,
% 2.96/3.16 (~r(s(s(s(z))), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[4696, 106, 2, 12715, 12157])).
% 2.96/3.16 tff(12717,plain,
% 2.96/3.16 (b(s(s(s(z))), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[2640, 25, 12716, 80])).
% 2.96/3.16 tff(12718,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12719,plain,
% 2.96/3.16 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12720,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12719])).
% 2.96/3.16 tff(12721,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12720, 12718])).
% 2.96/3.16 tff(12722,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12723,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12722, 12721])).
% 2.96/3.16 tff(12724,plain,
% 2.96/3.16 (~b(s(s(z)), s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12723, 171, 12713, 679, 666, 12717, 12687])).
% 2.96/3.16 tff(12725,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12726,plain,
% 2.96/3.16 (((~r(s(z), elem!1)) | (~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(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12727,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12726])).
% 2.96/3.16 tff(12728,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12727, 12725])).
% 2.96/3.16 tff(12729,plain,
% 2.96/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12730,plain,
% 2.96/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12729, 12728])).
% 2.96/3.16 tff(12731,plain,
% 2.96/3.16 (~r(s(s(z)), s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12730, 106, 2, 12715, 12157])).
% 2.96/3.16 tff(12732,plain,
% 2.96/3.16 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[979, 25, 12731])).
% 2.96/3.16 tff(12733,plain,
% 2.96/3.16 ($false),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12732, 12724, 900])).
% 2.96/3.16 tff(12734,plain,(b(s(s(s(z))), s(z)) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (s(z) = elem!1) | (elem!1 = s(s(z))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.96/3.16 tff(12735,plain,
% 2.96/3.16 (~b(s(s(z)), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12734, 12685, 1168, 2, 12158, 12159, 12156])).
% 2.96/3.16 tff(12736,plain,
% 2.96/3.16 (r(s(s(z)), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1416, 12735, 12151])).
% 2.96/3.16 tff(12737,plain,
% 2.96/3.16 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[785])).
% 2.96/3.16 tff(12738,plain,
% 2.96/3.16 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 2.96/3.16 inference(transitivity,[status(thm)],[12737, 3511])).
% 2.96/3.16 tff(12739,plain,
% 2.96/3.16 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12738])).
% 2.96/3.16 tff(12740,plain,
% 2.96/3.16 (~(z = elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[788, 785])).
% 2.96/3.16 tff(12741,plain,
% 2.96/3.16 (~(s(elem!1) = s(z))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[922, 12740])).
% 2.96/3.16 tff(12742,plain,
% 2.96/3.16 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[2184, 12741])).
% 2.96/3.16 tff(12743,plain,
% 2.96/3.16 (~(s(s(s(elem!1))) = elem!1)),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12742, 12739])).
% 2.96/3.16 tff(12744,plain,
% 2.96/3.16 (r(z, elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[651, 12740, 258])).
% 2.96/3.16 tff(12745,plain,
% 2.96/3.16 (~(elem!1 = z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[697, 12740])).
% 2.96/3.16 tff(12746,plain,
% 2.96/3.16 (r(elem!1, z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1567, 12745, 4070])).
% 2.96/3.16 tff(12747,plain,
% 2.96/3.16 (~r(s(s(s(elem!1))), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[4112, 12746, 3035, 12744])).
% 2.96/3.16 tff(12748,plain,
% 2.96/3.16 ($false),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[3859, 25, 12747, 5099, 12743])).
% 2.96/3.16 tff(12749,plain,((~(s(s(s(z))) = elem!1)) | b(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), z)) | b(elem!1, z) | b(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.96/3.16 tff(12750,plain,
% 2.96/3.16 (~(s(s(s(z))) = elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12749, 4070, 4369, 5099, 12328])).
% 2.96/3.16 tff(12751,plain,
% 2.96/3.16 (b(s(s(s(z))), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[804, 12685, 12750])).
% 2.96/3.16 tff(12752,plain,
% 2.96/3.16 (~(s(elem!1) = s(z))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[4379, 12751, 3045])).
% 2.96/3.16 tff(12753,plain,
% 2.96/3.16 (~(z = elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[703, 12752])).
% 2.96/3.16 tff(12754,plain,
% 2.96/3.16 (~(elem!1 = z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[697, 12753])).
% 2.96/3.16 tff(12755,plain,
% 2.96/3.16 (r(elem!1, z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1567, 12754, 4070])).
% 2.96/3.16 tff(12756,plain,
% 2.96/3.16 (~r(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[4864, 12755, 2, 12736])).
% 2.96/3.16 tff(12757,plain,
% 2.96/3.16 (b(s(z), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[1444, 12756, 12158])).
% 2.96/3.16 tff(12758,plain,
% 2.96/3.16 (~r(s(s(z)), z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12345, 12753, 676, 12144, 12328, 3281, 12736])).
% 2.96/3.16 tff(12759,plain,
% 2.96/3.16 (b(s(s(z)), z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[157, 12758])).
% 2.96/3.16 tff(12760,plain,
% 2.96/3.16 (~b(s(z), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[10236, 12759, 12144, 3281])).
% 2.96/3.16 tff(12761,plain,
% 2.96/3.16 (r(s(z), s(s(z)))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[550, 12760])).
% 2.96/3.16 tff(12762,plain,
% 2.96/3.16 ($false),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12315, 12761, 12757, 4070, 3281, 2, 12157, 5099, 3045, 6, 12156, 12151])).
% 2.96/3.16 tff(12763,plain,(b(s(s(s(z))), s(z)) | b(elem!1, z) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), z) | r(s(z), z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.16 tff(12764,plain,
% 2.96/3.16 (b(s(s(s(z))), s(z))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12763, 4070, 3281, 2, 5099, 3045, 6, 676])).
% 2.96/3.16 tff(12765,plain,
% 2.96/3.16 (~b(z, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[10773, 171, 3281, 12144, 12764])).
% 2.96/3.16 tff(12766,plain,
% 2.96/3.16 ((z = s(s(s(z)))) | r(z, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[8373, 25, 12765])).
% 2.96/3.16 tff(12767,plain,
% 2.96/3.16 (r(z, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12766, 8359])).
% 2.96/3.16 tff(12768,plain,
% 2.96/3.16 (~b(s(s(s(z))), z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[10291, 171, 3281, 12144, 12764])).
% 2.96/3.16 tff(12769,plain,
% 2.96/3.16 (r(s(s(s(z))), z)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[953, 25, 194, 12768])).
% 2.96/3.16 tff(12770,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12771,plain,
% 2.96/3.16 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12772,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12771])).
% 2.96/3.16 tff(12773,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12772, 12770])).
% 2.96/3.16 tff(12774,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12775,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(z)))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12774, 12773])).
% 2.96/3.16 tff(12776,plain,
% 2.96/3.16 ($false),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12775, 171, 679, 3281, 3133, 1188, 837])).
% 2.96/3.16 tff(12777,plain,((~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.16 tff(12778,plain,
% 2.96/3.16 (~b(s(s(s(z))), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12777, 12156, 3281, 12144, 12764])).
% 2.96/3.16 tff(12779,plain,
% 2.96/3.16 (r(s(s(s(z))), elem!1)),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[804, 12778, 12750])).
% 2.96/3.16 tff(12780,plain,
% 2.96/3.16 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[2102])).
% 2.96/3.16 tff(12781,plain,
% 2.96/3.16 (~(elem!1 = s(s(s(z))))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12750, 12780])).
% 2.96/3.16 tff(12782,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12783,plain,
% 2.96/3.16 (((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12784,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12783])).
% 2.96/3.16 tff(12785,plain,
% 2.96/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.16 inference(transitivity,[status(thm)],[12784, 12782])).
% 2.96/3.16 tff(12786,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))))),
% 2.96/3.16 inference(quant_inst,[status(thm)],[])).
% 2.96/3.16 tff(12787,plain,
% 2.96/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.96/3.16 inference(modus_ponens,[status(thm)],[12786, 12785])).
% 2.96/3.16 tff(12788,plain,
% 2.96/3.16 (~b(elem!1, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12787, 171, 12156, 3281, 12144, 12764])).
% 2.96/3.16 tff(12789,plain,
% 2.96/3.16 ((elem!1 = s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[939, 25, 12788])).
% 2.96/3.16 tff(12790,plain,
% 2.96/3.16 (r(elem!1, s(s(s(z))))),
% 2.96/3.16 inference(unit_resolution,[status(thm)],[12789, 12781])).
% 2.96/3.16 tff(12791,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12792,plain,
% 2.96/3.16 (((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.16 inference(rewrite,[status(thm)],[])).
% 2.96/3.16 tff(12793,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 2.96/3.16 inference(monotonicity,[status(thm)],[12792])).
% 2.96/3.16 tff(12794,plain,
% 2.96/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.17 inference(transitivity,[status(thm)],[12793, 12791])).
% 2.96/3.17 tff(12795,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 2.96/3.17 inference(quant_inst,[status(thm)],[])).
% 2.96/3.17 tff(12796,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12795, 12794])).
% 2.96/3.17 tff(12797,plain,
% 2.96/3.17 (~r(z, elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12796, 106, 12790, 12779, 12767])).
% 2.96/3.17 tff(12798,plain,
% 2.96/3.17 (z = elem!1),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[651, 12797, 12328])).
% 2.96/3.17 tff(12799,plain,
% 2.96/3.17 (~r(s(z), elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12676, 12798, 6])).
% 2.96/3.17 tff(12800,plain,
% 2.96/3.17 (b(s(z), elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1444, 12799, 12158])).
% 2.96/3.17 tff(12801,plain,
% 2.96/3.17 (s(elem!1) = s(z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[703, 12798])).
% 2.96/3.17 tff(12802,plain,
% 2.96/3.17 (~r(s(elem!1), z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12267, 12801, 6])).
% 2.96/3.17 tff(12803,plain,
% 2.96/3.17 (b(s(elem!1), z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1691, 12802])).
% 2.96/3.17 tff(12804,plain,
% 2.96/3.17 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12274, 12803, 3045])).
% 2.96/3.17 tff(12805,plain,
% 2.96/3.17 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12285, 12804])).
% 2.96/3.17 tff(12806,plain,
% 2.96/3.17 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1135, 12805, 12801])).
% 2.96/3.17 tff(12807,plain,
% 2.96/3.17 (~b(z, elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12327, 679, 3281, 3133])).
% 2.96/3.17 tff(12808,plain,
% 2.96/3.17 (~(s(s(s(z))) = elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12749, 4070, 3035, 5099, 12807])).
% 2.96/3.17 tff(12809,plain,
% 2.96/3.17 (~b(s(s(s(z))), elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12777, 679, 3281, 3133, 1188])).
% 2.96/3.17 tff(12810,plain,
% 2.96/3.17 (r(s(s(s(z))), elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[804, 12809, 12808])).
% 2.96/3.17 tff(12811,plain,
% 2.96/3.17 (~(elem!1 = s(s(s(z))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12808, 12780])).
% 2.96/3.17 tff(12812,plain,
% 2.96/3.17 (~b(elem!1, s(s(s(z))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12787, 171, 679, 3281, 3133, 1188])).
% 2.96/3.17 tff(12813,plain,
% 2.96/3.17 ((elem!1 = s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[939, 25, 12812])).
% 2.96/3.17 tff(12814,plain,
% 2.96/3.17 (r(elem!1, s(s(s(z))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12813, 12811])).
% 2.96/3.17 tff(12815,plain,
% 2.96/3.17 (~r(z, elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12796, 106, 12814, 12810, 10776])).
% 2.96/3.17 tff(12816,plain,
% 2.96/3.17 (z = elem!1),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[651, 12815, 12807])).
% 2.96/3.17 tff(12817,plain,
% 2.96/3.17 (s(elem!1) = s(z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[703, 12816])).
% 2.96/3.17 tff(12818,plain,
% 2.96/3.17 (~(s(s(s(s(z)))) = s(z))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[728, 12817])).
% 2.96/3.17 tff(12819,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12820,plain,
% 2.96/3.17 (((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12821,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12820])).
% 2.96/3.17 tff(12822,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 2.96/3.17 inference(transitivity,[status(thm)],[12821, 12819])).
% 2.96/3.17 tff(12823,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 2.96/3.17 inference(quant_inst,[status(thm)],[])).
% 2.96/3.17 tff(12824,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12823, 12822])).
% 2.96/3.17 tff(12825,plain,
% 2.96/3.17 (~r(elem!1, z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12824, 106, 12814, 12810, 10776])).
% 2.96/3.17 tff(12826,plain,
% 2.96/3.17 (elem!1 = z),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1567, 12825, 4070])).
% 2.96/3.17 tff(12827,plain,
% 2.96/3.17 (~r(z, elem!1)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12796, 106, 1426, 2049, 10776])).
% 2.96/3.17 tff(12828,plain,
% 2.96/3.17 (z = elem!1),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[651, 12827, 12807])).
% 2.96/3.17 tff(12829,plain,
% 2.96/3.17 (s(elem!1) = s(z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[703, 12828])).
% 2.96/3.17 tff(12830,plain,
% 2.96/3.17 (s(s(elem!1)) = s(s(z))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12829])).
% 2.96/3.17 tff(12831,plain,
% 2.96/3.17 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12830])).
% 2.96/3.17 tff(12832,plain,
% 2.96/3.17 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12831])).
% 2.96/3.17 tff(12833,plain,
% 2.96/3.17 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.96/3.17 inference(symmetry,[status(thm)],[12832])).
% 2.96/3.17 tff(12834,plain,
% 2.96/3.17 (r(s(s(elem!1)), s(s(s(s(s(z)))))) <=> r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[711])).
% 2.96/3.17 tff(12835,plain,
% 2.96/3.17 (r(s(s(z)), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(symmetry,[status(thm)],[12834])).
% 2.96/3.17 tff(12836,plain,
% 2.96/3.17 ((~r(s(s(z)), s(s(s(s(s(z))))))) <=> (~r(s(s(elem!1)), s(s(s(s(s(z)))))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12835])).
% 2.96/3.17 tff(12837,plain,
% 2.96/3.17 (~b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[3777, 840, 1421, 679])).
% 2.96/3.17 tff(12838,plain,
% 2.96/3.17 (r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[479, 12837])).
% 2.96/3.17 tff(12839,plain,
% 2.96/3.17 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[5772, 106, 554, 2, 12838])).
% 2.96/3.17 tff(12840,plain,
% 2.96/3.17 (~r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12839, 12836])).
% 2.96/3.17 tff(12841,plain,
% 2.96/3.17 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[9332, 106, 554, 2, 12838])).
% 2.96/3.17 tff(12842,plain,
% 2.96/3.17 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[225, 12841])).
% 2.96/3.17 tff(12843,plain,
% 2.96/3.17 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1890, 12842, 666, 840])).
% 2.96/3.17 tff(12844,plain,
% 2.96/3.17 (~b(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12449, 12843, 710])).
% 2.96/3.17 tff(12845,plain,
% 2.96/3.17 (r(s(s(elem!1)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[878, 12844, 4721])).
% 2.96/3.17 tff(12846,plain,
% 2.96/3.17 ($false),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12845, 12840])).
% 2.96/3.17 tff(12847,plain,((~b(elem!1, s(s(s(s(s(z))))))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.17 tff(12848,plain,
% 2.96/3.17 (~b(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12847, 666, 12829, 554, 2, 1421, 679])).
% 2.96/3.17 tff(12849,plain,
% 2.96/3.17 (r(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[782, 12848, 768])).
% 2.96/3.17 tff(12850,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12851,plain,
% 2.96/3.17 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z)))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12852,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12851])).
% 2.96/3.17 tff(12853,plain,
% 2.96/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.17 inference(transitivity,[status(thm)],[12852, 12850])).
% 2.96/3.17 tff(12854,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))))),
% 2.96/3.17 inference(quant_inst,[status(thm)],[])).
% 2.96/3.17 tff(12855,plain,
% 2.96/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12854, 12853])).
% 2.96/3.17 tff(12856,plain,
% 2.96/3.17 ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12855, 106])).
% 2.96/3.17 tff(12857,plain,
% 2.96/3.17 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12856, 12849, 2049, 1426])).
% 2.96/3.17 tff(12858,plain,
% 2.96/3.17 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1368, 12857])).
% 2.96/3.17 tff(12859,plain,
% 2.96/3.17 (b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12858, 12833])).
% 2.96/3.17 tff(12860,plain,
% 2.96/3.17 (r(z, s(s(s(s(s(z))))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12849, 1229])).
% 2.96/3.17 tff(12861,plain,
% 2.96/3.17 (~(s(s(s(s(z)))) = s(z))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[728, 710])).
% 2.96/3.17 tff(12862,plain,
% 2.96/3.17 (s(s(s(s(z)))) = s(z)),
% 2.96/3.17 inference(symmetry,[status(thm)],[249])).
% 2.96/3.17 tff(12863,plain,
% 2.96/3.17 (s(s(s(s(elem!1)))) = s(z)),
% 2.96/3.17 inference(transitivity,[status(thm)],[713, 12862])).
% 2.96/3.17 tff(12864,plain,
% 2.96/3.17 ($false),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[726, 12863])).
% 2.96/3.17 tff(12865,plain,((~(s(z) = s(s(s(s(z)))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.17 tff(12866,plain,
% 2.96/3.17 (~(s(z) = s(s(s(s(z)))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12865, 710])).
% 2.96/3.17 tff(12867,plain,
% 2.96/3.17 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[203, 25, 5773, 198])).
% 2.96/3.17 tff(12868,plain,
% 2.96/3.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[2018, 12867, 2010, 9334])).
% 2.96/3.17 tff(12869,plain,
% 2.96/3.17 (r(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1013, 12868])).
% 2.96/3.17 tff(12870,plain,
% 2.96/3.17 (r(s(s(s(z))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[995, 12869, 710])).
% 2.96/3.17 tff(12871,plain,
% 2.96/3.17 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[11463, 12870, 1188, 12866, 12861, 554, 2, 12451, 3133])).
% 2.96/3.17 tff(12872,plain,
% 2.96/3.17 (b(s(s(s(s(z)))), s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[374, 12871, 4725])).
% 2.96/3.17 tff(12873,plain,
% 2.96/3.17 (b(elem!1, s(s(z))) <=> b(z, s(s(z)))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[693])).
% 2.96/3.17 tff(12874,plain,
% 2.96/3.17 (~r(elem!1, s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12423, 12870, 2049, 2])).
% 2.96/3.17 tff(12875,plain,
% 2.96/3.17 (b(elem!1, s(s(z)))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[3154, 12874, 3122])).
% 2.96/3.17 tff(12876,plain,
% 2.96/3.17 (b(z, s(s(z)))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12875, 12873])).
% 2.96/3.17 tff(12877,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12878,plain,
% 2.96/3.17 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12879,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12878])).
% 2.96/3.17 tff(12880,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.96/3.17 inference(transitivity,[status(thm)],[12879, 12877])).
% 2.96/3.17 tff(12881,plain,
% 2.96/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)))),
% 2.96/3.17 inference(quant_inst,[status(thm)],[])).
% 2.96/3.17 tff(12882,plain,
% 2.96/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12881, 12880])).
% 2.96/3.17 tff(12883,plain,
% 2.96/3.17 (~b(s(s(s(s(z)))), z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12882, 171, 3281, 12876, 1, 12872])).
% 2.96/3.17 tff(12884,plain,
% 2.96/3.17 (r(s(s(s(s(z)))), z)),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[272, 25, 52, 12883])).
% 2.96/3.17 tff(12885,plain,
% 2.96/3.17 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[634, 12872, 1, 12876, 9334])).
% 2.96/3.17 tff(12886,plain,
% 2.96/3.17 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[426, 12885, 1314])).
% 2.96/3.17 tff(12887,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12888,plain,
% 2.96/3.17 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), 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(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.96/3.17 inference(rewrite,[status(thm)],[])).
% 2.96/3.17 tff(12889,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.96/3.17 inference(monotonicity,[status(thm)],[12888])).
% 2.96/3.17 tff(12890,plain,
% 2.96/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.96/3.17 inference(transitivity,[status(thm)],[12889, 12887])).
% 2.96/3.17 tff(12891,plain,
% 2.96/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.96/3.17 inference(quant_inst,[status(thm)],[])).
% 2.96/3.17 tff(12892,plain,
% 2.96/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.96/3.17 inference(modus_ponens,[status(thm)],[12891, 12890])).
% 2.96/3.17 tff(12893,plain,
% 2.96/3.17 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[12892, 171, 12876, 1, 9334, 12872])).
% 2.96/3.17 tff(12894,plain,
% 2.96/3.17 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[1156, 12893, 419])).
% 2.96/3.17 tff(12895,plain,
% 2.96/3.17 ($false),
% 2.96/3.17 inference(unit_resolution,[status(thm)],[8712, 106, 12894, 12886, 1288, 12884])).
% 2.96/3.17 tff(12896,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~r(z, s(s(s(s(s(z))))))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~(elem!1 = z)) | (elem!1 = s(s(z))) | (~r(s(s(s(z))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.18 tff(12897,plain,
% 2.96/3.18 (~r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12896, 12860, 419, 12237, 3281, 1188, 554, 2, 3133, 693, 3122, 2049, 12829, 12859])).
% 2.96/3.18 tff(12898,plain,
% 2.96/3.18 (b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[479, 12897])).
% 2.96/3.18 tff(12899,plain,
% 2.96/3.18 ($false),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[10902, 171, 3281, 3133, 1188, 12858, 12898])).
% 2.96/3.18 tff(12900,plain,((~b(s(s(z)), elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~(elem!1 = z)) | (elem!1 = s(s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.18 tff(12901,plain,
% 2.96/3.18 (~b(s(s(z)), elem!1)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12900, 554, 3133, 1188, 419, 3281, 2, 12826, 3738, 12810, 12814, 1421, 679])).
% 2.96/3.18 tff(12902,plain,
% 2.96/3.18 (r(s(s(z)), elem!1)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1416, 12901, 2116])).
% 2.96/3.18 tff(12903,plain,
% 2.96/3.18 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12826])).
% 2.96/3.18 tff(12904,plain,
% 2.96/3.18 (r(s(s(z)), z)),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12902, 12903])).
% 2.96/3.18 tff(12905,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12906,plain,
% 2.96/3.18 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12907,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12906])).
% 2.96/3.18 tff(12908,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12907, 12905])).
% 2.96/3.18 tff(12909,plain,
% 2.96/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.96/3.18 inference(quant_inst,[status(thm)],[])).
% 2.96/3.18 tff(12910,plain,
% 2.96/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12909, 12908])).
% 2.96/3.18 tff(12911,plain,
% 2.96/3.18 (~r(s(s(s(z))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12910, 106, 12904, 10784, 10776])).
% 2.96/3.18 tff(12912,plain,
% 2.96/3.18 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[995, 12911, 12817])).
% 2.96/3.18 tff(12913,plain,
% 2.96/3.18 (b(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1013, 12912])).
% 2.96/3.18 tff(12914,plain,
% 2.96/3.18 (b(s(s(s(z))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1020, 12913, 12817])).
% 2.96/3.18 tff(12915,plain,
% 2.96/3.18 (~r(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[10807, 106, 12904, 10784, 10776])).
% 2.96/3.18 tff(12916,plain,
% 2.96/3.18 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[979, 25, 12915])).
% 2.96/3.18 tff(12917,plain,
% 2.96/3.18 (b(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12916, 900])).
% 2.96/3.18 tff(12918,plain,
% 2.96/3.18 (~b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12234, 12917, 4070, 1421, 12914, 12902, 3829, 3035, 679, 3281, 5099])).
% 2.96/3.18 tff(12919,plain,
% 2.96/3.18 (r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[479, 12918])).
% 2.96/3.18 tff(12920,plain,
% 2.96/3.18 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[9332, 106, 554, 2, 12919])).
% 2.96/3.18 tff(12921,plain,
% 2.96/3.18 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[225, 12920])).
% 2.96/3.18 tff(12922,plain,
% 2.96/3.18 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[5772, 106, 554, 2, 12919])).
% 2.96/3.18 tff(12923,plain,
% 2.96/3.18 (b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[203, 25, 12922, 198])).
% 2.96/3.18 tff(12924,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(z))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12925,plain,
% 2.96/3.18 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), 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(z))))), s(s(s(z))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12926,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(z)))))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12925])).
% 2.96/3.18 tff(12927,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(z))))))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12926, 12924])).
% 2.96/3.18 tff(12928,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.96/3.18 inference(quant_inst,[status(thm)],[])).
% 2.96/3.18 tff(12929,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(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(z)))))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12928, 12927])).
% 2.96/3.18 tff(12930,plain,
% 2.96/3.18 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12929, 171, 12914, 12923, 12921])).
% 2.96/3.18 tff(12931,plain,
% 2.96/3.18 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1368, 12930])).
% 2.96/3.18 tff(12932,plain,
% 2.96/3.18 (z = elem!1),
% 2.96/3.18 inference(symmetry,[status(thm)],[12826])).
% 2.96/3.18 tff(12933,plain,
% 2.96/3.18 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12932])).
% 2.96/3.18 tff(12934,plain,
% 2.96/3.18 ((s(s(s(s(s(z))))) = z) <=> (elem!1 = s(s(s(s(s(z))))))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12933, 759])).
% 2.96/3.18 tff(12935,plain,
% 2.96/3.18 ((s(s(s(s(s(z))))) = z) <=> (s(s(s(s(s(z))))) = elem!1)),
% 2.96/3.18 inference(transitivity,[status(thm)],[12934, 760])).
% 2.96/3.18 tff(12936,plain,
% 2.96/3.18 ((~(s(s(s(s(s(z))))) = z)) <=> (~(s(s(s(s(s(z))))) = elem!1))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12935])).
% 2.96/3.18 tff(12937,plain,
% 2.96/3.18 (~(s(s(s(s(s(z))))) = elem!1)),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[140, 12936])).
% 2.96/3.18 tff(12938,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12939,plain,
% 2.96/3.18 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12940,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12939])).
% 2.96/3.18 tff(12941,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12940, 12938])).
% 2.96/3.18 tff(12942,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.96/3.18 inference(quant_inst,[status(thm)],[])).
% 2.96/3.18 tff(12943,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12942, 12941])).
% 2.96/3.18 tff(12944,plain,
% 2.96/3.18 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12943, 171, 12914, 12921, 12917])).
% 2.96/3.18 tff(12945,plain,
% 2.96/3.18 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[2614, 12944])).
% 2.96/3.18 tff(12946,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12947,plain,
% 2.96/3.18 (((~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12948,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12947])).
% 2.96/3.18 tff(12949,plain,
% 2.96/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12948, 12946])).
% 2.96/3.18 tff(12950,plain,
% 2.96/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.96/3.18 inference(quant_inst,[status(thm)],[])).
% 2.96/3.18 tff(12951,plain,
% 2.96/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12950, 12949])).
% 2.96/3.18 tff(12952,plain,
% 2.96/3.18 (~r(s(s(s(s(s(z))))), z)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12951, 106, 12945, 12931, 10776])).
% 2.96/3.18 tff(12953,plain,
% 2.96/3.18 (~r(s(s(s(s(s(z))))), elem!1)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[7842, 12952, 12816])).
% 2.96/3.18 tff(12954,plain,
% 2.96/3.18 (b(s(s(s(s(s(z))))), elem!1)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[853, 12953, 12937])).
% 2.96/3.18 tff(12955,plain,
% 2.96/3.18 (~b(s(z), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12643, 12954, 1421, 679])).
% 2.96/3.18 tff(12956,plain,
% 2.96/3.18 (r(s(z), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[60, 12955])).
% 2.96/3.18 tff(12957,plain,
% 2.96/3.18 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[820, 12817])).
% 2.96/3.18 tff(12958,plain,
% 2.96/3.18 (b(elem!1, s(s(s(s(s(z)))))) <=> b(z, s(s(s(s(s(z))))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12826])).
% 2.96/3.18 tff(12959,plain,
% 2.96/3.18 ((~(s(s(s(s(s(z))))) = z)) <=> (~(elem!1 = s(s(s(s(s(z)))))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12934])).
% 2.96/3.18 tff(12960,plain,
% 2.96/3.18 (~(elem!1 = s(s(s(s(s(z))))))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[140, 12959])).
% 2.96/3.18 tff(12961,plain,
% 2.96/3.18 (~r(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12856, 12931, 12810, 12814])).
% 2.96/3.18 tff(12962,plain,
% 2.96/3.18 (b(elem!1, s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[782, 12961, 12960])).
% 2.96/3.18 tff(12963,plain,
% 2.96/3.18 (b(z, s(s(s(s(s(z))))))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12962, 12958])).
% 2.96/3.18 tff(12964,plain,
% 2.96/3.18 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[5797, 12923, 2, 12921, 12963, 12957])).
% 2.96/3.18 tff(12965,plain,
% 2.96/3.18 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1156, 12964, 419])).
% 2.96/3.18 tff(12966,plain,
% 2.96/3.18 (~r(s(s(s(s(z)))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[2320, 106, 12965, 12956, 12931])).
% 2.96/3.18 tff(12967,plain,
% 2.96/3.18 (b(s(s(s(s(z)))), s(z))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[321, 12966, 12818])).
% 2.96/3.18 tff(12968,plain,
% 2.96/3.18 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1082, 12957])).
% 2.96/3.18 tff(12969,plain,
% 2.96/3.18 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[11437, 106, 12965, 12945, 12931])).
% 2.96/3.18 tff(12970,plain,
% 2.96/3.18 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[2842, 12969, 12968])).
% 2.96/3.18 tff(12971,plain,
% 2.96/3.18 (~(s(z) = s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12865, 12817])).
% 2.96/3.18 tff(12972,plain,
% 2.96/3.18 (~r(s(z), s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1363, 106, 12965, 12956, 12931])).
% 2.96/3.18 tff(12973,plain,
% 2.96/3.18 (b(s(z), s(s(s(s(z)))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[454, 12972, 12971])).
% 2.96/3.18 tff(12974,plain,
% 2.96/3.18 ($false),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[11461, 171, 3133, 1188, 12973, 12970, 12967])).
% 2.96/3.18 tff(12975,plain,((~r(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = s(s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | b(elem!1, z) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | b(s(s(s(elem!1))), elem!1) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.96/3.18 tff(12976,plain,
% 2.96/3.18 (~r(s(z), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12975, 12764, 12144, 12806, 2, 12800, 12156, 4070, 4369, 3281, 5099, 12151])).
% 2.96/3.18 tff(12977,plain,
% 2.96/3.18 (b(s(z), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[550, 12976])).
% 2.96/3.18 tff(12978,plain,
% 2.96/3.18 (~b(s(s(z)), z)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[10236, 12977, 12144, 3281])).
% 2.96/3.18 tff(12979,plain,
% 2.96/3.18 (r(s(s(z)), z)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[157, 12978])).
% 2.96/3.18 tff(12980,plain,
% 2.96/3.18 (~r(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[10807, 106, 12979, 12769, 12767])).
% 2.96/3.18 tff(12981,plain,
% 2.96/3.18 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[979, 25, 12980])).
% 2.96/3.18 tff(12982,plain,
% 2.96/3.18 (b(s(s(z)), s(s(s(z))))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12981, 900])).
% 2.96/3.18 tff(12983,plain,
% 2.96/3.18 (~r(s(s(s(z))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12910, 106, 12979, 12769, 12767])).
% 2.96/3.18 tff(12984,plain,
% 2.96/3.18 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[995, 12983, 12801])).
% 2.96/3.18 tff(12985,plain,
% 2.96/3.18 (b(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1013, 12984])).
% 2.96/3.18 tff(12986,plain,
% 2.96/3.18 (b(s(s(s(z))), s(s(z)))),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[1020, 12985, 12801])).
% 2.96/3.18 tff(12987,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12988,plain,
% 2.96/3.18 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12989,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12988])).
% 2.96/3.18 tff(12990,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.18 inference(transitivity,[status(thm)],[12989, 12987])).
% 2.96/3.18 tff(12991,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.96/3.18 inference(quant_inst,[status(thm)],[])).
% 2.96/3.18 tff(12992,plain,
% 2.96/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 2.96/3.18 inference(modus_ponens,[status(thm)],[12991, 12990])).
% 2.96/3.18 tff(12993,plain,
% 2.96/3.18 ($false),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12992, 171, 12977, 12764, 12986, 12982])).
% 2.96/3.18 tff(12994,plain,(b(elem!1, z) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), elem!1) | b(s(s(s(elem!1))), z) | r(s(z), z) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.18 tff(12995,plain,
% 2.96/3.18 (b(elem!1, z)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12994, 6, 2, 5099, 3045, 3281, 676])).
% 2.96/3.18 tff(12996,plain,
% 2.96/3.18 (b(z, elem!1)),
% 2.96/3.18 inference(unit_resolution,[status(thm)],[12340, 12995, 3281, 676, 12144])).
% 2.96/3.18 tff(12997,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12998,plain,
% 2.96/3.18 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))) <=> ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.96/3.18 inference(rewrite,[status(thm)],[])).
% 2.96/3.18 tff(12999,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))))),
% 2.96/3.18 inference(monotonicity,[status(thm)],[12998])).
% 2.96/3.18 tff(13000,plain,
% 2.96/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 2.96/3.19 inference(transitivity,[status(thm)],[12999, 12997])).
% 2.96/3.19 tff(13001,plain,
% 2.96/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13002,plain,
% 2.96/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, elem!1))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13001, 13000])).
% 2.96/3.19 tff(13003,plain,
% 2.96/3.19 ($false),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13002, 171, 3137, 1596, 679, 3133])).
% 2.96/3.19 tff(13004,plain,((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.19 tff(13005,plain,
% 2.96/3.19 (~b(elem!1, s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13004, 12996, 12995, 12144])).
% 2.96/3.19 tff(13006,plain,
% 2.96/3.19 (elem!1 = s(z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[687, 13005, 676])).
% 2.96/3.19 tff(13007,plain,
% 2.96/3.19 (s(elem!1) = s(s(z))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13006])).
% 2.96/3.19 tff(13008,plain,
% 2.96/3.19 (s(s(elem!1)) = s(s(s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13007])).
% 2.96/3.19 tff(13009,plain,
% 2.96/3.19 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13008])).
% 2.96/3.19 tff(13010,plain,
% 2.96/3.19 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13009])).
% 2.96/3.19 tff(13011,plain,
% 2.96/3.19 ((~(s(s(s(z))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13010])).
% 2.96/3.19 tff(13012,plain,
% 2.96/3.19 (~(z = elem!1)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[7338, 13005, 3281])).
% 2.96/3.19 tff(13013,plain,
% 2.96/3.19 (~(s(elem!1) = s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[922, 13012])).
% 2.96/3.19 tff(13014,plain,
% 2.96/3.19 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[2184, 13013])).
% 2.96/3.19 tff(13015,plain,
% 2.96/3.19 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13014, 13011])).
% 2.96/3.19 tff(13016,plain,
% 2.96/3.19 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13009])).
% 2.96/3.19 tff(13017,plain,
% 2.96/3.19 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13016])).
% 2.96/3.19 tff(13018,plain,
% 2.96/3.19 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 2.96/3.19 inference(symmetry,[status(thm)],[13017])).
% 2.96/3.19 tff(13019,plain,
% 2.96/3.19 (r(s(s(s(s(z)))), z)),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[4369, 13018])).
% 2.96/3.19 tff(13020,plain,
% 2.96/3.19 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13016])).
% 2.96/3.19 tff(13021,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13020])).
% 2.96/3.19 tff(13022,plain,
% 2.96/3.19 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13021])).
% 2.96/3.19 tff(13023,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[1008, 13022])).
% 2.96/3.19 tff(13024,plain,
% 2.96/3.19 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[2360])).
% 2.96/3.19 tff(13025,plain,
% 2.96/3.19 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13024, 2360])).
% 2.96/3.19 tff(13026,plain,
% 2.96/3.19 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13025, 416])).
% 2.96/3.19 tff(13027,plain,
% 2.96/3.19 ((s(s(s(s(z)))) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13026])).
% 2.96/3.19 tff(13028,plain,
% 2.96/3.19 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[404, 13027])).
% 2.96/3.19 tff(13029,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[2358])).
% 2.96/3.19 tff(13030,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13029])).
% 2.96/3.19 tff(13031,plain,
% 2.96/3.19 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13030])).
% 2.96/3.19 tff(13032,plain,
% 2.96/3.19 (~(s(s(s(elem!1))) = s(elem!1))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[1008, 13031])).
% 2.96/3.19 tff(13033,plain,
% 2.96/3.19 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[12285, 13032])).
% 2.96/3.19 tff(13034,plain,
% 2.96/3.19 ($false),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13033, 13028])).
% 2.96/3.19 tff(13035,plain,((~(s(s(s(s(z)))) = s(s(s(s(s(z))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.19 tff(13036,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13035, 13006])).
% 2.96/3.19 tff(13037,plain,
% 2.96/3.19 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[421, 13036])).
% 2.96/3.19 tff(13038,plain,
% 2.96/3.19 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(s(s(elem!1))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13016])).
% 2.96/3.19 tff(13039,plain,
% 2.96/3.19 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(z))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13038, 4561])).
% 2.96/3.19 tff(13040,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13039])).
% 2.96/3.19 tff(13041,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(s(z)))) = s(z))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13040, 247])).
% 2.96/3.19 tff(13042,plain,
% 2.96/3.19 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13041])).
% 2.96/3.19 tff(13043,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(z))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[818, 13042])).
% 2.96/3.19 tff(13044,plain,
% 2.96/3.19 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13009])).
% 2.96/3.19 tff(13045,plain,
% 2.96/3.19 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(z)))), s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13044])).
% 2.96/3.19 tff(13046,plain,
% 2.96/3.19 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13006])).
% 2.96/3.19 tff(13047,plain,
% 2.96/3.19 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13046])).
% 2.96/3.19 tff(13048,plain,
% 2.96/3.19 (~b(s(s(s(elem!1))), s(z))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[5099, 13047])).
% 2.96/3.19 tff(13049,plain,
% 2.96/3.19 (~b(s(s(s(s(z)))), s(z))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13048, 13045])).
% 2.96/3.19 tff(13050,plain,
% 2.96/3.19 (r(s(s(s(s(z)))), s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[319, 25, 13049, 13043])).
% 2.96/3.19 tff(13051,plain,
% 2.96/3.19 (~b(s(s(s(z))), s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[10925, 13050, 3281, 13037, 12144, 2, 13023, 13019, 13015])).
% 2.96/3.19 tff(13052,plain,
% 2.96/3.19 (r(s(s(s(z))), s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[1173, 13051])).
% 2.96/3.19 tff(13053,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[4229, 13015])).
% 2.96/3.19 tff(13054,plain,
% 2.96/3.19 (r(s(s(s(s(s(z))))), z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[145, 10388])).
% 2.96/3.19 tff(13055,plain,
% 2.96/3.19 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[2361])).
% 2.96/3.19 tff(13056,plain,
% 2.96/3.19 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.96/3.19 inference(symmetry,[status(thm)],[13055])).
% 2.96/3.19 tff(13057,plain,
% 2.96/3.19 ((~(s(s(s(elem!1))) = s(s(z)))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13056])).
% 2.96/3.19 tff(13058,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[1008, 13057])).
% 2.96/3.19 tff(13059,plain,
% 2.96/3.19 (~(s(s(s(s(z)))) = s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13035, 1428])).
% 2.96/3.19 tff(13060,plain,
% 2.96/3.19 (((~r(z, s(s(s(s(s(z))))))) | (~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)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13061,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13060])).
% 2.96/3.19 tff(13062,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z))))))))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13061, 9413])).
% 2.96/3.19 tff(13063,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~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))))))))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13064,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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))))))) | (~r(z, s(s(s(s(s(z)))))))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13063, 13062])).
% 2.96/3.19 tff(13065,plain,
% 2.96/3.19 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13064, 106, 13054, 10381, 2118])).
% 2.96/3.19 tff(13066,plain,
% 2.96/3.19 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[1156, 13065, 13059])).
% 2.96/3.19 tff(13067,plain,
% 2.96/3.19 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[10410, 106, 637, 127, 1288])).
% 2.96/3.19 tff(13068,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13069,plain,
% 2.96/3.19 (((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13070,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z)))))))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13069])).
% 2.96/3.19 tff(13071,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z))))))))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13070, 13068])).
% 2.96/3.19 tff(13072,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(z))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13073,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(s(s(z)))))))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13072, 13071])).
% 2.96/3.19 tff(13074,plain,
% 2.96/3.19 (~r(s(s(s(s(z)))), s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13073, 106, 637, 1288, 2118])).
% 2.96/3.19 tff(13075,plain,
% 2.96/3.19 (b(s(s(s(s(z)))), s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[374, 13074, 369])).
% 2.96/3.19 tff(13076,plain,
% 2.96/3.19 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[5760, 13075, 3686, 207])).
% 2.96/3.19 tff(13077,plain,
% 2.96/3.19 ($false),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[203, 25, 13076, 13067, 198])).
% 2.96/3.19 tff(13078,plain,((~r(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(z)))) | (s(s(s(s(z)))) = s(s(z))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.19 tff(13079,plain,
% 2.96/3.19 (~r(s(s(z)), z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13078, 207, 13066, 13058, 10381, 2118, 13054])).
% 2.96/3.19 tff(13080,plain,
% 2.96/3.19 (b(s(s(z)), z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[157, 13079])).
% 2.96/3.19 tff(13081,plain,
% 2.96/3.19 (~b(s(z), s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[10236, 13080, 3133, 3281])).
% 2.96/3.19 tff(13082,plain,
% 2.96/3.19 (r(s(z), s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[550, 13081])).
% 2.96/3.19 tff(13083,plain,
% 2.96/3.19 (~b(z, s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[11405, 13082, 13058, 263, 747, 2, 13080])).
% 2.96/3.19 tff(13084,plain,
% 2.96/3.19 (r(z, s(s(z)))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[124, 13083])).
% 2.96/3.19 tff(13085,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13086,plain,
% 2.96/3.19 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13087,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13086])).
% 2.96/3.19 tff(13088,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13087, 13085])).
% 2.96/3.19 tff(13089,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13090,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13089, 13088])).
% 2.96/3.19 tff(13091,plain,
% 2.96/3.19 (~r(s(s(s(elem!1))), z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13090, 106, 2, 991, 600])).
% 2.96/3.19 tff(13092,plain,
% 2.96/3.19 (b(s(s(s(elem!1))), z)),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[1578, 25, 724, 13091])).
% 2.96/3.19 tff(13093,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13094,plain,
% 2.96/3.19 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13095,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13094])).
% 2.96/3.19 tff(13096,plain,
% 2.96/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13095, 13093])).
% 2.96/3.19 tff(13097,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13098,plain,
% 2.96/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.96/3.19 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 2.96/3.19 tff(13099,plain,
% 2.96/3.19 (~r(s(s(s(elem!1))), s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[13098, 106, 554, 2, 991])).
% 2.96/3.19 tff(13100,plain,
% 2.96/3.19 (b(s(s(s(elem!1))), s(z))),
% 2.96/3.19 inference(unit_resolution,[status(thm)],[1807, 13099])).
% 2.96/3.19 tff(13101,plain,
% 2.96/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13102,plain,
% 2.96/3.19 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 2.96/3.19 inference(rewrite,[status(thm)],[])).
% 2.96/3.19 tff(13103,plain,
% 2.96/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1))))),
% 2.96/3.19 inference(monotonicity,[status(thm)],[13102])).
% 2.96/3.19 tff(13104,plain,
% 2.96/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 2.96/3.19 inference(transitivity,[status(thm)],[13103, 13101])).
% 2.96/3.19 tff(13105,plain,
% 2.96/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.96/3.19 inference(quant_inst,[status(thm)],[])).
% 2.96/3.19 tff(13106,plain,
% 2.96/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, elem!1))),
% 2.96/3.20 inference(modus_ponens,[status(thm)],[13105, 13104])).
% 2.96/3.20 tff(13107,plain,
% 2.96/3.20 ($false),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[13106, 171, 3137, 13100, 3281, 3133, 13092])).
% 2.96/3.20 tff(13108,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.20 tff(13109,plain,
% 2.96/3.20 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[13108, 13084, 2, 3281, 3133, 3137, 13082])).
% 2.96/3.20 tff(13110,plain,
% 2.96/3.20 (b(s(s(s(elem!1))), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[1013, 13109])).
% 2.96/3.20 tff(13111,plain,
% 2.96/3.20 (b(s(s(s(s(z)))), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[2902, 13110, 1428])).
% 2.96/3.20 tff(13112,plain,
% 2.96/3.20 ($false),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[6057, 171, 3281, 13080, 13066, 4, 207, 13111])).
% 2.96/3.20 tff(13113,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~(elem!1 = s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.20 tff(13114,plain,
% 2.96/3.20 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[13113, 4, 3281, 1428, 2, 3133, 3137, 263, 747, 2118])).
% 2.96/3.20 tff(13115,plain,
% 2.96/3.20 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[225, 13114])).
% 2.96/3.20 tff(13116,plain,
% 2.96/3.20 (~r(s(s(z)), z)),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[10397, 13115, 4, 3281, 3133])).
% 2.96/3.20 tff(13117,plain,
% 2.96/3.20 (b(s(s(z)), z)),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[157, 13116])).
% 2.96/3.20 tff(13118,plain,
% 2.96/3.20 (~b(s(z), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[10236, 13117, 3133, 3281])).
% 2.96/3.20 tff(13119,plain,
% 2.96/3.20 (r(s(z), s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[550, 13118])).
% 2.96/3.20 tff(13120,plain,
% 2.96/3.20 (~b(z, s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[11405, 13119, 13058, 263, 747, 2, 13117])).
% 2.96/3.20 tff(13121,plain,
% 2.96/3.20 (r(z, s(s(z)))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[124, 13120])).
% 2.96/3.20 tff(13122,plain,
% 2.96/3.20 ($false),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[6027, 106, 2, 13121, 13115, 13054])).
% 2.96/3.20 tff(13123,plain,((~b(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~(elem!1 = s(z))) | (~b(z, elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 2.96/3.20 tff(13124,plain,
% 2.96/3.20 (~b(s(s(s(s(s(z))))), s(z))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[13123, 13050, 2, 13052, 12144, 3281, 13006, 12996, 13019])).
% 2.96/3.20 tff(13125,plain,
% 2.96/3.20 (r(s(s(s(s(s(z))))), s(z))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[479, 13124])).
% 2.96/3.20 tff(13126,plain,
% 2.96/3.20 (~r(s(z), s(s(s(s(s(z))))))),
% 2.96/3.20 inference(unit_resolution,[status(thm)],[5763, 13036, 13023, 13125, 13050, 2])).
% 3.04/3.20 tff(13127,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[60, 13126])).
% 3.04/3.20 tff(13128,plain,
% 3.04/3.20 (~b(s(s(s(s(s(z))))), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8383, 13127, 12144, 3281])).
% 3.04/3.20 tff(13129,plain,
% 3.04/3.20 (r(s(s(s(s(s(z))))), z)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[145, 13128])).
% 3.04/3.20 tff(13130,plain,
% 3.04/3.20 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(z))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13006])).
% 3.04/3.20 tff(13131,plain,
% 3.04/3.20 ((s(s(s(z))) = s(z)) <=> (s(s(s(z))) = elem!1)),
% 3.04/3.20 inference(symmetry,[status(thm)],[13130])).
% 3.04/3.20 tff(13132,plain,
% 3.04/3.20 ((~(s(s(s(z))) = s(z))) <=> (~(s(s(s(z))) = elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13131])).
% 3.04/3.20 tff(13133,plain,
% 3.04/3.20 (~(s(s(s(z))) = elem!1)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[344, 13132])).
% 3.04/3.20 tff(13134,plain,
% 3.04/3.20 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(z))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13006])).
% 3.04/3.20 tff(13135,plain,
% 3.04/3.20 (b(s(s(s(z))), s(z)) <=> b(s(s(s(z))), elem!1)),
% 3.04/3.20 inference(symmetry,[status(thm)],[13134])).
% 3.04/3.20 tff(13136,plain,
% 3.04/3.20 ((~b(s(s(s(z))), s(z))) <=> (~b(s(s(s(z))), elem!1))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13135])).
% 3.04/3.20 tff(13137,plain,
% 3.04/3.20 (~b(s(s(s(z))), elem!1)),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13051, 13136])).
% 3.04/3.20 tff(13138,plain,
% 3.04/3.20 (r(s(s(s(z))), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[804, 13137, 13133])).
% 3.04/3.20 tff(13139,plain,
% 3.04/3.20 ((s(z) = s(s(s(s(z))))) <=> (s(z) = s(s(s(elem!1))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[2361])).
% 3.04/3.20 tff(13140,plain,
% 3.04/3.20 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(z))),
% 3.04/3.20 inference(transitivity,[status(thm)],[13139, 4561])).
% 3.04/3.20 tff(13141,plain,
% 3.04/3.20 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 3.04/3.20 inference(symmetry,[status(thm)],[13140])).
% 3.04/3.20 tff(13142,plain,
% 3.04/3.20 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13141])).
% 3.04/3.20 tff(13143,plain,
% 3.04/3.20 (~(s(z) = s(s(s(s(z)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[818, 13142])).
% 3.04/3.20 tff(13144,plain,
% 3.04/3.20 (~r(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8203, 260, 502, 263])).
% 3.04/3.20 tff(13145,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[454, 13144, 13143])).
% 3.04/3.20 tff(13146,plain,
% 3.04/3.20 ((~b(elem!1, s(s(s(z))))) <=> (~b(s(z), s(s(s(z)))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[4168])).
% 3.04/3.20 tff(13147,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 3.04/3.20 inference(symmetry,[status(thm)],[4091])).
% 3.04/3.20 tff(13148,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[376, 13147])).
% 3.04/3.20 tff(13149,plain,
% 3.04/3.20 (~(s(s(s(s(s(z))))) = s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[421, 13059])).
% 3.04/3.20 tff(13150,plain,
% 3.04/3.20 (~r(z, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[10522, 1357, 127, 747])).
% 3.04/3.20 tff(13151,plain,
% 3.04/3.20 ((z = s(s(s(z)))) | b(z, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8373, 25, 13150])).
% 3.04/3.20 tff(13152,plain,
% 3.04/3.20 (b(z, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13151, 8359])).
% 3.04/3.20 tff(13153,plain,
% 3.04/3.20 (~r(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8573, 1357, 502, 747])).
% 3.04/3.20 tff(13154,plain,
% 3.04/3.20 (b(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1996, 13153])).
% 3.04/3.20 tff(13155,plain,
% 3.04/3.20 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8563, 13154, 376, 260, 1357, 2839, 502])).
% 3.04/3.20 tff(13156,plain,
% 3.04/3.20 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2614, 13155])).
% 3.04/3.20 tff(13157,plain,
% 3.04/3.20 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[9285, 13156, 13154, 3281, 376, 13152])).
% 3.04/3.20 tff(13158,plain,
% 3.04/3.20 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[426, 13157, 13149])).
% 3.04/3.20 tff(13159,plain,
% 3.04/3.20 (~b(elem!1, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12474, 13158, 2049, 2839, 13148, 1357, 260])).
% 3.04/3.20 tff(13160,plain,
% 3.04/3.20 (~b(s(z), s(s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13159, 13146])).
% 3.04/3.20 tff(13161,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13154, 13160])).
% 3.04/3.20 tff(13162,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), elem!1)) | (s(s(s(z))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13163,plain,
% 3.04/3.20 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13162, 13145, 2049, 2839, 260, 3281, 1428, 502, 127, 747])).
% 3.04/3.20 tff(13164,plain,
% 3.04/3.20 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1368, 13163])).
% 3.04/3.20 tff(13165,plain,
% 3.04/3.20 (~r(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2312, 260, 502, 263])).
% 3.04/3.20 tff(13166,plain,
% 3.04/3.20 (b(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1996, 13165])).
% 3.04/3.20 tff(13167,plain,
% 3.04/3.20 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8446, 13166, 1275, 13164])).
% 3.04/3.20 tff(13168,plain,
% 3.04/3.20 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2614, 13167])).
% 3.04/3.20 tff(13169,plain,
% 3.04/3.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8535, 13168, 502, 260])).
% 3.04/3.20 tff(13170,plain,
% 3.04/3.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2842, 13169, 2839])).
% 3.04/3.20 tff(13171,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13145, 13147])).
% 3.04/3.20 tff(13172,plain,
% 3.04/3.20 (b(elem!1, s(s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13166, 4169])).
% 3.04/3.20 tff(13173,plain,
% 3.04/3.20 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8620, 106, 260, 13168, 502])).
% 3.04/3.20 tff(13174,plain,
% 3.04/3.20 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4240, 25, 13173, 8230])).
% 3.04/3.20 tff(13175,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12092, 13174, 13172, 13171, 13170])).
% 3.04/3.20 tff(13176,plain,((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (s(s(s(z))) = s(s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13177,plain,
% 3.04/3.20 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13176, 13006, 13125, 13015, 13127, 13050, 13138, 3281, 13129, 13052])).
% 3.04/3.20 tff(13178,plain,
% 3.04/3.20 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1156, 13177, 13036])).
% 3.04/3.20 tff(13179,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(s(z))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[1275, 4843])).
% 3.04/3.20 tff(13180,plain,
% 3.04/3.20 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8446, 1976, 1275, 1384])).
% 3.04/3.20 tff(13181,plain,
% 3.04/3.20 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2614, 13180])).
% 3.04/3.20 tff(13182,plain,
% 3.04/3.20 (~r(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8219, 13181, 502, 747])).
% 3.04/3.20 tff(13183,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[454, 13182, 13143])).
% 3.04/3.20 tff(13184,plain,
% 3.04/3.20 (~b(z, s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[10690, 3686, 3281, 1976, 1384, 376])).
% 3.04/3.20 tff(13185,plain,
% 3.04/3.20 ((z = s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[291, 25, 13184])).
% 3.04/3.20 tff(13186,plain,
% 3.04/3.20 (r(z, s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13185, 5641])).
% 3.04/3.20 tff(13187,plain,
% 3.04/3.20 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12504, 3686, 840, 2433])).
% 3.04/3.20 tff(13188,plain,
% 3.04/3.20 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[426, 13187, 10875])).
% 3.04/3.20 tff(13189,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[10915, 106, 13188, 13186, 127, 263])).
% 3.04/3.20 tff(13190,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (s(s(s(s(s(z))))) = s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13191,plain,
% 3.04/3.20 (~b(elem!1, s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13190, 13183, 263, 3281, 127, 3686, 1384, 13149, 13179, 1976])).
% 3.04/3.20 tff(13192,plain,
% 3.04/3.20 (~b(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13191, 4092])).
% 3.04/3.20 tff(13193,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13183, 13192])).
% 3.04/3.20 tff(13194,plain,((~b(s(z), s(s(s(z))))) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(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(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13195,plain,
% 3.04/3.20 (~b(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13194, 1384, 263, 3281, 127, 3686, 1428, 502, 747, 1275])).
% 3.04/3.20 tff(13196,plain,
% 3.04/3.20 (r(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1996, 13195])).
% 3.04/3.20 tff(13197,plain,
% 3.04/3.20 (~r(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8246, 1384, 2839, 3686, 747, 502])).
% 3.04/3.20 tff(13198,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[454, 13197, 13143])).
% 3.04/3.20 tff(13199,plain,
% 3.04/3.20 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[10752, 13198, 1275, 1384, 3686])).
% 3.04/3.20 tff(13200,plain,
% 3.04/3.20 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2614, 13199])).
% 3.04/3.20 tff(13201,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12570, 106, 13200, 502, 13196, 747])).
% 3.04/3.20 tff(13202,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (s(s(s(z))) = s(s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13203,plain,
% 3.04/3.20 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13202, 13125, 13052, 13127, 13178, 13015, 13050, 3281, 13129, 13006])).
% 3.04/3.20 tff(13204,plain,
% 3.04/3.20 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1368, 13203])).
% 3.04/3.20 tff(13205,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(s(z)))))) <=> b(s(z), s(s(s(s(s(z))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13006])).
% 3.04/3.20 tff(13206,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(s(z)))))) <=> b(elem!1, s(s(s(s(s(z))))))),
% 3.04/3.20 inference(symmetry,[status(thm)],[13205])).
% 3.04/3.20 tff(13207,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(s(z))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13127, 13206])).
% 3.04/3.20 tff(13208,plain,
% 3.04/3.20 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13040])).
% 3.04/3.20 tff(13209,plain,
% 3.04/3.20 (~(s(z) = s(s(s(s(z)))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[818, 13208])).
% 3.04/3.20 tff(13210,plain,
% 3.04/3.20 (~r(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8213, 13204, 13125, 13052])).
% 3.04/3.20 tff(13211,plain,
% 3.04/3.20 (b(s(z), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[454, 13210, 13209])).
% 3.04/3.20 tff(13212,plain,
% 3.04/3.20 (b(elem!1, s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4096, 13211, 13006])).
% 3.04/3.20 tff(13213,plain,
% 3.04/3.20 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12504, 13212, 13207, 13178])).
% 3.04/3.20 tff(13214,plain,
% 3.04/3.20 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[426, 13213, 13037])).
% 3.04/3.20 tff(13215,plain,
% 3.04/3.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12068, 13214, 13050, 13204])).
% 3.04/3.20 tff(13216,plain,
% 3.04/3.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2842, 13215, 13015])).
% 3.04/3.20 tff(13217,plain,
% 3.04/3.20 ((elem!1 = s(s(elem!1))) <=> (s(z) = s(s(s(z))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13006, 13008])).
% 3.04/3.20 tff(13218,plain,
% 3.04/3.20 ((elem!1 = s(s(elem!1))) <=> (s(s(s(z))) = s(z))),
% 3.04/3.20 inference(transitivity,[status(thm)],[13217, 4075])).
% 3.04/3.20 tff(13219,plain,
% 3.04/3.20 ((s(s(s(z))) = s(z)) <=> (elem!1 = s(s(elem!1)))),
% 3.04/3.20 inference(symmetry,[status(thm)],[13218])).
% 3.04/3.20 tff(13220,plain,
% 3.04/3.20 ((~(s(s(s(z))) = s(z))) <=> (~(elem!1 = s(s(elem!1))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13219])).
% 3.04/3.20 tff(13221,plain,
% 3.04/3.20 (~(elem!1 = s(s(elem!1)))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[344, 13220])).
% 3.04/3.20 tff(13222,plain,
% 3.04/3.20 (~r(s(z), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8573, 13204, 13125, 13052])).
% 3.04/3.20 tff(13223,plain,
% 3.04/3.20 (~r(elem!1, s(s(elem!1)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4206, 13222, 13006])).
% 3.04/3.20 tff(13224,plain,
% 3.04/3.20 (b(elem!1, s(s(elem!1)))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4200, 13223, 13221])).
% 3.04/3.20 tff(13225,plain,
% 3.04/3.20 (b(elem!1, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4174, 13224, 13006])).
% 3.04/3.20 tff(13226,plain,
% 3.04/3.20 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[12092, 13225, 13212, 13216])).
% 3.04/3.20 tff(13227,plain,
% 3.04/3.20 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[4240, 25, 13226, 13053])).
% 3.04/3.20 tff(13228,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[8841, 106, 13214, 13204, 13227, 13052])).
% 3.04/3.20 tff(13229,plain,(r(s(z), z) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), elem!1) | r(elem!1, s(z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13230,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13229, 12143, 12140, 3281, 2, 6, 12134])).
% 3.04/3.20 tff(13231,plain,((~(s(z) = elem!1)) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | r(s(z), z) | b(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13232,plain,
% 3.04/3.20 (~(s(z) = elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13231, 12058, 3281, 12130, 12046, 2])).
% 3.04/3.20 tff(13233,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~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)))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13234,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~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)))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(13235,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13234, 13233])).
% 3.04/3.20 tff(13236,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13235, 106, 2, 1446, 11997, 396])).
% 3.04/3.20 tff(13237,plain,((~r(s(z), elem!1)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13238,plain,
% 3.04/3.20 (~r(s(z), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13237, 396, 2])).
% 3.04/3.20 tff(13239,plain,
% 3.04/3.20 (b(s(z), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[1444, 13238, 13232])).
% 3.04/3.20 tff(13240,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13241,plain,
% 3.04/3.20 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13242,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13241])).
% 3.04/3.20 tff(13243,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[13242, 13240])).
% 3.04/3.20 tff(13244,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(13245,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13244, 13243])).
% 3.04/3.20 tff(13246,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13245, 106, 2049, 5609, 769, 2604])).
% 3.04/3.20 tff(13247,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13248,plain,
% 3.04/3.20 (~r(s(s(s(z))), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13247, 769, 5609, 2604])).
% 3.04/3.20 tff(13249,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13250,plain,
% 3.04/3.20 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13251,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13250])).
% 3.04/3.20 tff(13252,plain,
% 3.04/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[13251, 13249])).
% 3.04/3.20 tff(13253,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(elem!1, s(s(s(z))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.20 tff(13254,plain,
% 3.04/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.20 inference(modus_ponens,[status(thm)],[13253, 13252])).
% 3.04/3.20 tff(13255,plain,
% 3.04/3.20 ($false),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13254, 106, 1426, 5609, 769, 2604])).
% 3.04/3.20 tff(13256,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.20 tff(13257,plain,
% 3.04/3.20 (~r(elem!1, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[13256, 769, 5609, 2604])).
% 3.04/3.20 tff(13258,plain,
% 3.04/3.20 (~(elem!1 = s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[2149, 797])).
% 3.04/3.20 tff(13259,plain,
% 3.04/3.20 (b(elem!1, s(s(s(z))))),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[940, 13258])).
% 3.04/3.20 tff(13260,plain,
% 3.04/3.20 (b(s(s(s(z))), elem!1)),
% 3.04/3.20 inference(unit_resolution,[status(thm)],[804, 797, 799])).
% 3.04/3.20 tff(13261,plain,
% 3.04/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13262,plain,
% 3.04/3.20 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.20 inference(rewrite,[status(thm)],[])).
% 3.04/3.20 tff(13263,plain,
% 3.04/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 3.04/3.20 inference(monotonicity,[status(thm)],[13262])).
% 3.04/3.20 tff(13264,plain,
% 3.04/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.20 inference(transitivity,[status(thm)],[13263, 13261])).
% 3.04/3.20 tff(13265,plain,
% 3.04/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.20 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13266,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13265, 13264])).
% 3.04/3.21 tff(13267,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13266, 171, 1421, 1976, 13260, 13259])).
% 3.04/3.21 tff(13268,plain,((s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13269,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13268, 13257, 13248, 11701, 1421, 797])).
% 3.04/3.21 tff(13270,plain,((~r(elem!1, s(s(s(s(s(z))))))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13271,plain,
% 3.04/3.21 (~r(elem!1, s(s(s(s(s(z))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13270, 13239, 12129, 12045, 12076])).
% 3.04/3.21 tff(13272,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 3.04/3.21 tff(13273,plain,
% 3.04/3.21 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13272])).
% 3.04/3.21 tff(13274,plain,
% 3.04/3.21 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(z))), elem!1)),
% 3.04/3.21 inference(symmetry,[status(thm)],[13273])).
% 3.04/3.21 tff(13275,plain,
% 3.04/3.21 ((~r(s(s(s(z))), s(s(s(s(z)))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13274])).
% 3.04/3.21 tff(13276,plain,
% 3.04/3.21 (~r(s(s(s(z))), elem!1)),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[2838, 13275])).
% 3.04/3.21 tff(13277,plain,
% 3.04/3.21 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13272])).
% 3.04/3.21 tff(13278,plain,
% 3.04/3.21 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.04/3.21 inference(symmetry,[status(thm)],[13277])).
% 3.04/3.21 tff(13279,plain,
% 3.04/3.21 ((~r(s(s(s(s(z)))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13278])).
% 3.04/3.21 tff(13280,plain,
% 3.04/3.21 (~r(elem!1, s(s(s(z))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[6473, 13279])).
% 3.04/3.21 tff(13281,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1426, 13280])).
% 3.04/3.21 tff(13282,plain,((~(elem!1 = s(s(s(s(z)))))) | (~r(elem!1, s(s(s(z))))) | r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13283,plain,
% 3.04/3.21 (~r(elem!1, s(s(s(z))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13282, 13272, 6473])).
% 3.04/3.21 tff(13284,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13285,plain,
% 3.04/3.21 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13286,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13285])).
% 3.04/3.21 tff(13287,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[13286, 13284])).
% 3.04/3.21 tff(13288,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13289,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(z)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13288, 13287])).
% 3.04/3.21 tff(13290,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13289, 171, 3137, 1421, 3133, 13260, 13259])).
% 3.04/3.21 tff(13291,plain,((s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13292,plain,
% 3.04/3.21 ((s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | r(elem!1, s(s(s(z)))) | r(s(s(s(z))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13291, 9835])).
% 3.04/3.21 tff(13293,plain,
% 3.04/3.21 (r(s(s(s(z))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13292, 13283, 1421, 797, 3137])).
% 3.04/3.21 tff(13294,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13293, 13276])).
% 3.04/3.21 tff(13295,plain,((~(elem!1 = s(s(s(s(z)))))) | r(s(s(s(z))), s(s(s(s(z))))) | (~b(s(z), elem!1)) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | r(s(s(s(s(z)))), s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13296,plain,
% 3.04/3.21 (~(elem!1 = s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13295, 13239, 12069, 12129, 12106, 12073])).
% 3.04/3.21 tff(13297,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13298,plain,
% 3.04/3.21 (((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13299,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13298])).
% 3.04/3.21 tff(13300,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[13299, 13297])).
% 3.04/3.21 tff(13301,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(z))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13302,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13301, 13300])).
% 3.04/3.21 tff(13303,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13302, 171, 3137, 3281, 1421, 3686, 1275, 2433])).
% 3.04/3.21 tff(13304,plain,((~b(elem!1, s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13305,plain,
% 3.04/3.21 (~b(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13304, 13239, 10693, 3281, 3686, 12106])).
% 3.04/3.21 tff(13306,plain,
% 3.04/3.21 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[2445, 25, 13305])).
% 3.04/3.21 tff(13307,plain,
% 3.04/3.21 (r(elem!1, s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13306, 13296])).
% 3.04/3.21 tff(13308,plain,
% 3.04/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13309,plain,
% 3.04/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13310,plain,
% 3.04/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13309, 13308])).
% 3.04/3.21 tff(13311,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13310, 106, 5609, 2027, 263, 2448])).
% 3.04/3.21 tff(13312,plain,((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13313,plain,
% 3.04/3.21 (~r(s(s(s(s(s(z))))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13312, 13307, 12045, 12047])).
% 3.04/3.21 tff(13314,assumption,(~r(s(s(s(s(s(z))))), elem!1)), introduced(assumption)).
% 3.04/3.21 tff(13315,plain,
% 3.04/3.21 (elem!1 = s(s(s(s(s(z)))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[7845, 759])).
% 3.04/3.21 tff(13316,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[1908, 13315])).
% 3.04/3.21 tff(13317,plain,((~(s(s(s(s(s(z))))) = elem!1)) | (elem!1 = s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13318,plain,
% 3.04/3.21 (~(s(s(s(s(s(z))))) = elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13317, 1908])).
% 3.04/3.21 tff(13319,plain,
% 3.04/3.21 (b(s(s(s(s(s(z))))), elem!1)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[853, 13318, 13314])).
% 3.04/3.21 tff(13320,assumption,(~r(elem!1, s(s(s(s(s(z))))))), introduced(assumption)).
% 3.04/3.21 tff(13321,plain,
% 3.04/3.21 (b(elem!1, s(s(s(s(s(z))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[782, 1908, 13320])).
% 3.04/3.21 tff(13322,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13323,plain,
% 3.04/3.21 (((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13324,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13323])).
% 3.04/3.21 tff(13325,plain,
% 3.04/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[13324, 13322])).
% 3.04/3.21 tff(13326,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(s(s(z))))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z)))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13327,plain,
% 3.04/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(z))))), elem!1)) | (~b(elem!1, s(s(s(s(s(z)))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13326, 13325])).
% 3.04/3.21 tff(13328,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13327, 171, 3137, 1421, 9835, 13321, 13319])).
% 3.04/3.21 tff(13329,plain,((elem!1 = s(s(s(s(s(z)))))) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | r(s(s(s(s(s(z))))), elem!1) | r(elem!1, s(s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13330,plain,
% 3.04/3.21 (elem!1 = s(s(s(s(s(z)))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13329, 13313, 13239, 12106, 13271])).
% 3.04/3.21 tff(13331,plain,
% 3.04/3.21 (s(elem!1) = s(s(s(s(s(s(z))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13330])).
% 3.04/3.21 tff(13332,plain,
% 3.04/3.21 (s(s(elem!1)) = s(s(s(s(s(s(s(z)))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13331])).
% 3.04/3.21 tff(13333,plain,
% 3.04/3.21 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(z))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13332])).
% 3.04/3.21 tff(13334,plain,
% 3.04/3.21 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 3.04/3.21 inference(symmetry,[status(thm)],[13333])).
% 3.04/3.21 tff(13335,plain,
% 3.04/3.21 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13334])).
% 3.04/3.21 tff(13336,plain,
% 3.04/3.21 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.21 inference(symmetry,[status(thm)],[13335])).
% 3.04/3.21 tff(13337,plain,
% 3.04/3.21 ((z = s(s(s(s(s(s(s(s(z))))))))) <=> (s(s(s(s(s(s(s(s(z)))))))) = z)),
% 3.04/3.21 inference(commutativity,[status(thm)],[])).
% 3.04/3.21 tff(13338,plain,
% 3.04/3.21 ((s(s(s(s(s(s(s(s(z)))))))) = z) <=> (z = s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.21 inference(symmetry,[status(thm)],[13337])).
% 3.04/3.21 tff(13339,plain,
% 3.04/3.21 ((~(s(s(s(s(s(s(s(s(z)))))))) = z)) <=> (~(z = s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13338])).
% 3.04/3.21 tff(13340,plain,
% 3.04/3.21 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(z)))))))) = z))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13341,plain,
% 3.04/3.21 (~(s(s(s(s(s(s(s(s(z)))))))) = z)),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13340, 13])).
% 3.04/3.21 tff(13342,plain,
% 3.04/3.21 (~(z = s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13341, 13339])).
% 3.04/3.21 tff(13343,assumption,(r(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.04/3.21 tff(13344,plain,
% 3.04/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13345,plain,
% 3.04/3.21 (((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.21 inference(rewrite,[status(thm)],[])).
% 3.04/3.21 tff(13346,plain,
% 3.04/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))))),
% 3.04/3.21 inference(monotonicity,[status(thm)],[13345])).
% 3.04/3.21 tff(13347,plain,
% 3.04/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(z, s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.21 inference(transitivity,[status(thm)],[13346, 13344])).
% 3.04/3.21 tff(13348,plain,
% 3.04/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 3.04/3.21 inference(quant_inst,[status(thm)],[])).
% 3.04/3.21 tff(13349,plain,
% 3.04/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.21 inference(modus_ponens,[status(thm)],[13348, 13347])).
% 3.04/3.21 tff(13350,plain,
% 3.04/3.21 ($false),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13349, 106, 637, 396, 127, 13343])).
% 3.04/3.21 tff(13351,plain,((~r(z, s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.21 tff(13352,plain,
% 3.04/3.21 (~r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.21 inference(unit_resolution,[status(thm)],[13351, 396, 12051, 10696])).
% 3.04/3.21 tff(13353,plain,
% 3.04/3.21 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(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(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13354,plain,
% 3.04/3.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(13355,plain,
% 3.04/3.22 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z))))))))) | r(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13354, 13353])).
% 3.04/3.22 tff(13356,plain,
% 3.04/3.22 ((z = s(s(s(s(s(s(s(s(z))))))))) | b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13355, 25, 13352])).
% 3.04/3.22 tff(13357,plain,
% 3.04/3.22 (b(z, s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13356, 13342])).
% 3.04/3.22 tff(13358,plain,
% 3.04/3.22 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[7170, 501, 5609, 263])).
% 3.04/3.22 tff(13359,plain,
% 3.04/3.22 (b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[351, 13358])).
% 3.04/3.22 tff(13360,plain,
% 3.04/3.22 (~r(s(s(z)), s(s(s(z))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[8875, 106, 5609, 2604, 501])).
% 3.04/3.22 tff(13361,plain,
% 3.04/3.22 (b(s(s(z)), s(s(s(z))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[10462, 13360])).
% 3.04/3.22 tff(13362,plain,
% 3.04/3.22 (~r(s(s(s(z))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[8882, 106, 5609, 2604, 501])).
% 3.04/3.22 tff(13363,plain,
% 3.04/3.22 (b(s(s(s(z))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[2642, 13362])).
% 3.04/3.22 tff(13364,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[11172, 13363, 13361, 6462, 13359])).
% 3.04/3.22 tff(13365,plain,((~r(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13366,plain,
% 3.04/3.22 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13365, 12074, 12045, 12076, 12047])).
% 3.04/3.22 tff(13367,plain,
% 3.04/3.22 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[205, 13366])).
% 3.04/3.22 tff(13368,plain,
% 3.04/3.22 (r(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(z), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13334])).
% 3.04/3.22 tff(13369,plain,
% 3.04/3.22 ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(s(z), s(s(s(elem!1)))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13368])).
% 3.04/3.22 tff(13370,assumption,(r(s(z), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.04/3.22 tff(13371,plain,
% 3.04/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13372,plain,
% 3.04/3.22 (((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~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))))) <=> ((~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)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13373,plain,
% 3.04/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13372])).
% 3.04/3.22 tff(13374,plain,
% 3.04/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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)))) | (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[13373, 13371])).
% 3.04/3.22 tff(13375,plain,
% 3.04/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~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)))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(13376,plain,
% 3.04/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13375, 13374])).
% 3.04/3.22 tff(13377,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13376, 106, 2, 11997, 396, 13370])).
% 3.04/3.22 tff(13378,plain,((~r(s(z), s(s(s(s(s(s(s(s(z)))))))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13379,plain,
% 3.04/3.22 (~r(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13378, 396, 2])).
% 3.04/3.22 tff(13380,plain,
% 3.04/3.22 (~r(s(z), s(s(s(elem!1))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13379, 13369])).
% 3.04/3.22 tff(13381,plain,
% 3.04/3.22 (b(s(z), s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[2229, 13380])).
% 3.04/3.22 tff(13382,assumption,(b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))), introduced(assumption)).
% 3.04/3.22 tff(13383,plain,
% 3.04/3.22 (s(s(s(s(s(s(s(s(z)))))))) = s(s(s(elem!1)))),
% 3.04/3.22 inference(symmetry,[status(thm)],[3505])).
% 3.04/3.22 tff(13384,plain,
% 3.04/3.22 (b(s(z), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(z), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13383])).
% 3.04/3.22 tff(13385,plain,
% 3.04/3.22 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[13384])).
% 3.04/3.22 tff(13386,plain,
% 3.04/3.22 (b(s(z), s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[2209, 13385])).
% 3.04/3.22 tff(13387,assumption,(b(z, s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.04/3.22 tff(13388,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(z)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13389,plain,
% 3.04/3.22 (((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(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(z)))) <=> ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13390,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13389])).
% 3.04/3.22 tff(13391,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(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(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), 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(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[13390, 13388])).
% 3.04/3.22 tff(13392,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(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(z))))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(13393,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13392, 13391])).
% 3.04/3.22 tff(13394,plain,
% 3.04/3.22 ((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13393, 171, 3281, 10693, 160, 13387])).
% 3.04/3.22 tff(13395,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13394, 13386, 13382])).
% 3.04/3.22 tff(13396,plain,((~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(z), s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13397,plain,
% 3.04/3.22 (~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13396, 13381, 13367, 13357, 3281, 13330])).
% 3.04/3.22 tff(13398,plain,
% 3.04/3.22 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13383])).
% 3.04/3.22 tff(13399,plain,
% 3.04/3.22 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.22 inference(symmetry,[status(thm)],[13398])).
% 3.04/3.22 tff(13400,plain,
% 3.04/3.22 (b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[1016, 13399])).
% 3.04/3.22 tff(13401,assumption,(~b(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))), introduced(assumption)).
% 3.04/3.22 tff(13402,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13401, 13400])).
% 3.04/3.22 tff(13403,plain,((~b(s(s(s(elem!1))), s(s(z)))) | b(s(s(s(s(s(s(s(s(z)))))))), s(s(z))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13404,plain,
% 3.04/3.22 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13403, 13397, 13330])).
% 3.04/3.22 tff(13405,plain,
% 3.04/3.22 (r(s(s(s(elem!1))), s(s(z)))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[1013, 13404])).
% 3.04/3.22 tff(13406,plain,
% 3.04/3.22 (r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13405, 13336])).
% 3.04/3.22 tff(13407,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(s(z))))), elem!1)),
% 3.04/3.22 inference(monotonicity,[status(thm)],[1418])).
% 3.04/3.22 tff(13408,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), elem!1) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.22 inference(symmetry,[status(thm)],[13407])).
% 3.04/3.22 tff(13409,plain,
% 3.04/3.22 ((~r(s(s(s(s(s(z))))), elem!1)) <=> (~r(s(s(s(s(s(z))))), s(s(z))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13408])).
% 3.04/3.22 tff(13410,plain,
% 3.04/3.22 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13314, 13409])).
% 3.04/3.22 tff(13411,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[396, 13410])).
% 3.04/3.22 tff(13412,plain,((~(s(s(z)) = elem!1)) | (~r(s(s(s(s(s(z))))), s(s(z)))) | r(s(s(s(s(s(z))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13413,plain,
% 3.04/3.22 (~(s(s(z)) = elem!1)),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13412, 13313, 396])).
% 3.04/3.22 tff(13414,plain,
% 3.04/3.22 (~(s(s(s(s(s(z))))) = s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3828, 13413])).
% 3.04/3.22 tff(13415,plain,
% 3.04/3.22 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13330])).
% 3.04/3.22 tff(13416,plain,
% 3.04/3.22 (b(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[13415])).
% 3.04/3.22 tff(13417,plain,
% 3.04/3.22 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13334])).
% 3.04/3.22 tff(13418,plain,
% 3.04/3.22 (b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[13417, 13416])).
% 3.04/3.22 tff(13419,plain,
% 3.04/3.22 ((~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13418])).
% 3.04/3.22 tff(13420,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.04/3.22 tff(13421,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13422,plain,
% 3.04/3.22 (((~b(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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13423,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13422])).
% 3.04/3.22 tff(13424,plain,
% 3.04/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[13423, 13421])).
% 3.04/3.22 tff(13425,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 3.04/3.22 inference(quant_inst,[status(thm)],[])).
% 3.04/3.22 tff(13426,plain,
% 3.04/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(s(s(z)))))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13425, 13424])).
% 3.04/3.22 tff(13427,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13426, 171, 9835, 3686, 376, 2527, 13387, 13420])).
% 3.04/3.22 tff(13428,plain,((~b(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(z))))))) | (~b(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))))))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13429,plain,
% 3.04/3.22 (~b(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13428, 13357, 12043, 12061, 3686])).
% 3.04/3.22 tff(13430,plain,
% 3.04/3.22 (~b(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13429, 13419])).
% 3.04/3.22 tff(13431,plain,
% 3.04/3.22 (r(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[3301, 13430, 13330, 13414])).
% 3.04/3.22 tff(13432,plain,
% 3.04/3.22 (r(elem!1, s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[3077])).
% 3.04/3.22 tff(13433,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(symmetry,[status(thm)],[13432])).
% 3.04/3.22 tff(13434,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(s(s(s(s(s(z))))), s(s(s(elem!1))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13383])).
% 3.04/3.22 tff(13435,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(transitivity,[status(thm)],[13434, 13433])).
% 3.04/3.22 tff(13436,plain,
% 3.04/3.22 ((~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 3.04/3.22 inference(monotonicity,[status(thm)],[13435])).
% 3.04/3.22 tff(13437,assumption,(~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))), introduced(assumption)).
% 3.04/3.22 tff(13438,plain,
% 3.04/3.22 (~r(elem!1, s(s(s(elem!1))))),
% 3.04/3.22 inference(modus_ponens,[status(thm)],[13437, 13436])).
% 3.04/3.22 tff(13439,plain,
% 3.04/3.22 ($false),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[1652, 13438])).
% 3.04/3.22 tff(13440,plain,(r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~(elem!1 = s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.22 tff(13441,plain,
% 3.04/3.22 (r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z)))))))))),
% 3.04/3.22 inference(unit_resolution,[status(thm)],[13440, 13431, 13330])).
% 3.04/3.22 tff(13442,plain,
% 3.04/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13443,plain,
% 3.04/3.22 (((~r(s(s(z)), s(z))) | (~r(s(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(s(z))))))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.22 inference(rewrite,[status(thm)],[])).
% 3.04/3.22 tff(13444,plain,
% 3.04/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(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(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(s(z))))))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13443])).
% 3.04/3.23 tff(13445,plain,
% 3.04/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(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(s(z)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(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(s(z))))), s(s(s(s(s(s(s(s(z)))))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13444, 13442])).
% 3.04/3.23 tff(13446,plain,
% 3.04/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(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(s(z)))))))))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13447,plain,
% 3.04/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(s(s(s(s(z))))))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13446, 13445])).
% 3.04/3.23 tff(13448,plain,
% 3.04/3.23 (~r(s(s(s(s(s(s(s(s(z)))))))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13447, 106, 2, 396, 13441])).
% 3.04/3.23 tff(13449,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13448, 13406])).
% 3.04/3.23 tff(13450,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13451,plain,
% 3.04/3.23 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13450, 3281, 3686, 2])).
% 3.04/3.23 tff(13452,plain,
% 3.04/3.23 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[225, 13451])).
% 3.04/3.23 tff(13453,plain,
% 3.04/3.23 ((~r(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(z)))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13078, 355])).
% 3.04/3.23 tff(13454,plain,
% 3.04/3.23 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13453, 13452, 3686, 12059, 12051, 10696])).
% 3.04/3.23 tff(13455,plain,
% 3.04/3.23 (~b(z, s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[10600, 13452, 2, 3686, 13367])).
% 3.04/3.23 tff(13456,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[498, 13455, 13454])).
% 3.04/3.23 tff(13457,plain,((~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13458,plain,
% 3.04/3.23 (~b(z, s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13457, 3686, 2])).
% 3.04/3.23 tff(13459,plain,
% 3.04/3.23 (r(z, s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[93, 13458])).
% 3.04/3.23 tff(13460,plain,
% 3.04/3.23 (~r(s(z), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[11520, 1, 96])).
% 3.04/3.23 tff(13461,plain,
% 3.04/3.23 (b(s(z), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[550, 13460])).
% 3.04/3.23 tff(13462,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13463,plain,
% 3.04/3.23 (((~b(s(s(z)), z)) | (~b(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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z))))) <=> ((~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13464,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13463])).
% 3.04/3.23 tff(13465,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13464, 13462])).
% 3.04/3.23 tff(13466,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(z)))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13467,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13466, 13465])).
% 3.04/3.23 tff(13468,plain,
% 3.04/3.23 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13467, 171, 13461, 1, 10693, 207])).
% 3.04/3.23 tff(13469,plain,
% 3.04/3.23 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[205, 13468])).
% 3.04/3.23 tff(13470,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13471,plain,
% 3.04/3.23 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13472,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13471])).
% 3.04/3.23 tff(13473,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), 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(z), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13472, 13470])).
% 3.04/3.23 tff(13474,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13475,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13474, 13473])).
% 3.04/3.23 tff(13476,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13475, 171, 1, 9835, 3686, 10693, 207, 357])).
% 3.04/3.23 tff(13477,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(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(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13478,plain,
% 3.04/3.23 (~b(s(s(s(s(z)))), s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13477, 1, 3686, 207])).
% 3.04/3.23 tff(13479,plain,
% 3.04/3.23 (r(s(s(s(s(z)))), s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[9955, 13478])).
% 3.04/3.23 tff(13480,plain,
% 3.04/3.23 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8521, 3686, 10693, 376])).
% 3.04/3.23 tff(13481,plain,
% 3.04/3.23 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[427, 13480])).
% 3.04/3.23 tff(13482,plain,
% 3.04/3.23 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8446, 838, 10693, 11701])).
% 3.04/3.23 tff(13483,plain,
% 3.04/3.23 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1368, 13482])).
% 3.04/3.23 tff(13484,plain,
% 3.04/3.23 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[12068, 13483, 5609, 263])).
% 3.04/3.23 tff(13485,plain,
% 3.04/3.23 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[10361, 13484])).
% 3.04/3.23 tff(13486,plain,
% 3.04/3.23 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8853, 13485, 376, 838, 11701])).
% 3.04/3.23 tff(13487,plain,
% 3.04/3.23 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[6475, 13486])).
% 3.04/3.23 tff(13488,plain,
% 3.04/3.23 (~r(s(s(s(z))), s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8843, 13487, 5609, 13483])).
% 3.04/3.23 tff(13489,plain,
% 3.04/3.23 (b(s(s(s(z))), s(z))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1173, 13488])).
% 3.04/3.23 tff(13490,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13491,plain,
% 3.04/3.23 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13492,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13491])).
% 3.04/3.23 tff(13493,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13492, 13490])).
% 3.04/3.23 tff(13494,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13495,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13494, 13493])).
% 3.04/3.23 tff(13496,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13495, 171, 1, 9835, 13489, 838, 10693, 207])).
% 3.04/3.23 tff(13497,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13498,plain,
% 3.04/3.23 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13497, 1, 207, 13481, 376, 13479])).
% 3.04/3.23 tff(13499,plain,
% 3.04/3.23 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[2614, 13498])).
% 3.04/3.23 tff(13500,plain,
% 3.04/3.23 (~r(s(s(z)), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8875, 106, 13481, 13499, 13469])).
% 3.04/3.23 tff(13501,plain,
% 3.04/3.23 (b(s(s(z)), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[10462, 13500])).
% 3.04/3.23 tff(13502,plain,
% 3.04/3.23 (~r(s(s(s(z))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8882, 106, 13481, 13499, 13469])).
% 3.04/3.23 tff(13503,plain,
% 3.04/3.23 (b(s(s(s(z))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[2642, 13502])).
% 3.04/3.23 tff(13504,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13505,plain,
% 3.04/3.23 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13506,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13505])).
% 3.04/3.23 tff(13507,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13506, 13504])).
% 3.04/3.23 tff(13508,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13509,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z)))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13508, 13507])).
% 3.04/3.23 tff(13510,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13509, 171, 13461, 1, 13503, 11701, 13501])).
% 3.04/3.23 tff(13511,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13512,plain,
% 3.04/3.23 (~b(s(s(z)), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13511, 207, 12043, 3686, 13459])).
% 3.04/3.23 tff(13513,plain,
% 3.04/3.23 (r(s(s(z)), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[157, 13512])).
% 3.04/3.23 tff(13514,plain,
% 3.04/3.23 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[5760, 160, 3686, 207])).
% 3.04/3.23 tff(13515,plain,
% 3.04/3.23 (r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[9958, 13514])).
% 3.04/3.23 tff(13516,plain,
% 3.04/3.23 (~r(s(s(s(s(z)))), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[6904, 13515, 13459, 13513])).
% 3.04/3.23 tff(13517,plain,
% 3.04/3.23 (b(s(s(s(s(z)))), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[274, 13516])).
% 3.04/3.23 tff(13518,plain,
% 3.04/3.23 (~b(z, s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[10600, 160, 2, 3686, 207])).
% 3.04/3.23 tff(13519,plain,
% 3.04/3.23 (r(z, s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[498, 13518])).
% 3.04/3.23 tff(13520,plain,
% 3.04/3.23 (~r(z, s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[7972, 13519, 12045, 13515])).
% 3.04/3.23 tff(13521,plain,
% 3.04/3.23 (b(z, s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[293, 13520])).
% 3.04/3.23 tff(13522,plain,
% 3.04/3.23 (((~b(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(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.23 inference(rewrite,[status(thm)],[])).
% 3.04/3.23 tff(13523,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.04/3.23 inference(monotonicity,[status(thm)],[13522])).
% 3.04/3.23 tff(13524,plain,
% 3.04/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.23 inference(transitivity,[status(thm)],[13523, 10197])).
% 3.04/3.23 tff(13525,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 3.04/3.23 inference(quant_inst,[status(thm)],[])).
% 3.04/3.23 tff(13526,plain,
% 3.04/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.04/3.23 inference(modus_ponens,[status(thm)],[13525, 13524])).
% 3.04/3.23 tff(13527,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13526, 171, 9835, 12043, 13521, 13517])).
% 3.04/3.23 tff(13528,plain,((~b(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.23 tff(13529,plain,
% 3.04/3.23 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13528, 207, 3686, 2])).
% 3.04/3.23 tff(13530,plain,
% 3.04/3.23 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[205, 13529])).
% 3.04/3.23 tff(13531,plain,
% 3.04/3.23 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[7170, 263, 13481, 501])).
% 3.04/3.23 tff(13532,plain,
% 3.04/3.23 (b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[351, 13531])).
% 3.04/3.23 tff(13533,plain,
% 3.04/3.23 (~b(s(s(z)), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13511, 207, 376, 3686, 96])).
% 3.04/3.23 tff(13534,plain,
% 3.04/3.23 (r(s(s(z)), z)),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[157, 13533])).
% 3.04/3.23 tff(13535,plain,
% 3.04/3.23 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[13365, 6462, 5609, 501, 263])).
% 3.04/3.23 tff(13536,plain,
% 3.04/3.23 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[2614, 13535])).
% 3.04/3.23 tff(13537,plain,
% 3.04/3.23 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8446, 13536, 10693, 11701])).
% 3.04/3.23 tff(13538,plain,
% 3.04/3.23 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[1368, 13537])).
% 3.04/3.23 tff(13539,plain,
% 3.04/3.23 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[8853, 13536, 376, 6462, 11701])).
% 3.04/3.23 tff(13540,plain,
% 3.04/3.23 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[10361, 13539])).
% 3.04/3.23 tff(13541,plain,
% 3.04/3.23 ($false),
% 3.04/3.23 inference(unit_resolution,[status(thm)],[12068, 13540, 13538, 5609, 263])).
% 3.04/3.23 tff(13542,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13543,plain,
% 3.04/3.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13542, 263, 13481, 376, 501])).
% 3.04/3.24 tff(13544,plain,
% 3.04/3.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[6475, 13543])).
% 3.04/3.24 tff(13545,plain,
% 3.04/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13546,plain,
% 3.04/3.24 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~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(z)))), 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)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13547,plain,
% 3.04/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[13546])).
% 3.04/3.24 tff(13548,plain,
% 3.04/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[13547, 13545])).
% 3.04/3.24 tff(13549,plain,
% 3.04/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13550,plain,
% 3.04/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13549, 13548])).
% 3.04/3.24 tff(13551,plain,
% 3.04/3.24 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13550, 106, 5609, 5567, 6477])).
% 3.04/3.24 tff(13552,plain,
% 3.04/3.24 (b(z, s(s(s(s(s(z))))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[498, 13551])).
% 3.04/3.24 tff(13553,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13554,plain,
% 3.04/3.24 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13555,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[13554])).
% 3.04/3.24 tff(13556,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.24 inference(transitivity,[status(thm)],[13555, 13553])).
% 3.04/3.24 tff(13557,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13558,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13557, 13556])).
% 3.04/3.24 tff(13559,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13558, 171, 9835, 10693, 207, 11674, 13552])).
% 3.04/3.24 tff(13560,plain,((~r(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13561,plain,
% 3.04/3.24 (~r(z, s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13560, 13544, 13481, 207, 263])).
% 3.04/3.24 tff(13562,plain,
% 3.04/3.24 (b(z, s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[293, 13561])).
% 3.04/3.24 tff(13563,plain,
% 3.04/3.24 (~b(s(s(s(s(z)))), z)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[10351, 171, 9835, 3686, 376, 13562])).
% 3.04/3.24 tff(13564,plain,
% 3.04/3.24 (r(s(s(s(s(z)))), z)),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[274, 13563])).
% 3.04/3.24 tff(13565,plain,
% 3.04/3.24 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[6904, 13564, 96, 13534])).
% 3.04/3.24 tff(13566,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[9958, 13565])).
% 3.04/3.24 tff(13567,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13568,plain,
% 3.04/3.24 (((~b(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(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13569,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[13568])).
% 3.04/3.24 tff(13570,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[13569, 13567])).
% 3.04/3.24 tff(13571,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13572,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13571, 13570])).
% 3.04/3.24 tff(13573,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13572, 171, 3686, 207, 13566, 13532])).
% 3.04/3.24 tff(13574,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13575,plain,
% 3.04/3.24 (~r(s(s(s(s(z)))), s(z))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13574, 207, 3686, 13459, 12043, 13530])).
% 3.04/3.24 tff(13576,plain,
% 3.04/3.24 (b(s(s(s(s(z)))), s(z))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[9955, 13575])).
% 3.04/3.24 tff(13577,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13578,plain,
% 3.04/3.24 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13579,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[13578])).
% 3.04/3.24 tff(13580,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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)))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[13579, 13577])).
% 3.04/3.24 tff(13581,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13582,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13581, 13580])).
% 3.04/3.24 tff(13583,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13582, 171, 11701, 376, 2852, 357])).
% 3.04/3.24 tff(13584,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13585,plain,
% 3.04/3.24 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13584, 13576, 12043])).
% 3.04/3.24 tff(13586,plain,
% 3.04/3.24 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[10361, 13585])).
% 3.04/3.24 tff(13587,plain,
% 3.04/3.24 (~r(s(z), s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[9881, 13513, 2, 13459])).
% 3.04/3.24 tff(13588,plain,
% 3.04/3.24 (b(s(z), s(s(z)))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[550, 13587])).
% 3.04/3.24 tff(13589,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13590,plain,
% 3.04/3.24 (((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13591,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.24 inference(monotonicity,[status(thm)],[13590])).
% 3.04/3.24 tff(13592,plain,
% 3.04/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.24 inference(transitivity,[status(thm)],[13591, 13589])).
% 3.04/3.24 tff(13593,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13594,plain,
% 3.04/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13593, 13592])).
% 3.04/3.24 tff(13595,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13594, 171, 323, 11701, 838, 6462, 207, 357])).
% 3.04/3.24 tff(13596,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13597,plain,
% 3.04/3.24 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13596, 838, 323, 207, 357])).
% 3.04/3.24 tff(13598,plain,
% 3.04/3.24 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[6475, 13597])).
% 3.04/3.24 tff(13599,plain,
% 3.04/3.24 (~r(s(s(s(z))), s(z))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[8843, 13598, 5609, 13483])).
% 3.04/3.24 tff(13600,plain,
% 3.04/3.24 (b(s(s(s(z))), s(z))),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[1173, 13599])).
% 3.04/3.24 tff(13601,plain,
% 3.04/3.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.04/3.24 inference(rewrite,[status(thm)],[])).
% 3.04/3.24 tff(13602,plain,
% 3.04/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.04/3.24 inference(quant_inst,[status(thm)],[])).
% 3.04/3.24 tff(13603,plain,
% 3.04/3.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.04/3.24 inference(modus_ponens,[status(thm)],[13602, 13601])).
% 3.04/3.24 tff(13604,plain,
% 3.04/3.24 ($false),
% 3.04/3.24 inference(unit_resolution,[status(thm)],[13603, 106, 5609, 1357, 6477, 2828])).
% 3.04/3.24 tff(13605,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.24 tff(13606,plain,
% 3.04/3.24 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13605, 13598, 5609, 13483])).
% 3.04/3.25 tff(13607,plain,
% 3.04/3.25 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[10361, 13606])).
% 3.04/3.25 tff(13608,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[8545, 13607, 13600, 376, 357])).
% 3.04/3.25 tff(13609,plain,((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13610,plain,
% 3.04/3.25 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13609, 13576, 12043, 12045, 13588, 207])).
% 3.04/3.25 tff(13611,plain,
% 3.04/3.25 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2614, 13610])).
% 3.04/3.25 tff(13612,plain,
% 3.04/3.25 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[11880, 2118, 96, 637])).
% 3.04/3.25 tff(13613,plain,
% 3.04/3.25 (b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[351, 13612])).
% 3.04/3.25 tff(13614,plain,
% 3.04/3.25 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[6904, 2118, 96, 637])).
% 3.04/3.25 tff(13615,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[9958, 13614])).
% 3.04/3.25 tff(13616,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13617,plain,
% 3.04/3.25 (((~b(s(s(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(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), 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(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13618,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[13617])).
% 3.04/3.25 tff(13619,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[13618, 13616])).
% 3.04/3.25 tff(13620,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(13621,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[13620, 13619])).
% 3.04/3.25 tff(13622,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13621, 171, 323, 3686, 10693, 357, 13615, 13613])).
% 3.04/3.25 tff(13623,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13624,plain,
% 3.04/3.25 (~r(s(s(s(s(z)))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13623, 13576, 3686, 13588, 13459, 13513])).
% 3.04/3.25 tff(13625,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[274, 13624])).
% 3.04/3.25 tff(13626,plain,
% 3.04/3.25 (~b(z, s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[11906, 13625, 13576])).
% 3.04/3.25 tff(13627,plain,
% 3.04/3.25 (r(z, s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[293, 13626])).
% 3.04/3.25 tff(13628,plain,
% 3.04/3.25 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[10937, 5567, 5609, 6477])).
% 3.04/3.25 tff(13629,plain,
% 3.04/3.25 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[145, 13628])).
% 3.04/3.25 tff(13630,plain,
% 3.04/3.25 (~b(z, s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[8932, 13629, 10693, 3686, 357])).
% 3.04/3.25 tff(13631,plain,
% 3.04/3.25 (r(z, s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[498, 13630])).
% 3.04/3.25 tff(13632,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13550, 106, 5609, 5567, 6477, 13631])).
% 3.04/3.25 tff(13633,plain,((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13634,plain,
% 3.04/3.25 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13633, 13627, 12045, 3686, 13576])).
% 3.04/3.25 tff(13635,plain,
% 3.04/3.25 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[6475, 13634])).
% 3.04/3.25 tff(13636,plain,
% 3.04/3.25 (~b(s(s(s(z))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[8894, 13360, 6462, 356])).
% 3.04/3.25 tff(13637,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2642, 13636, 13362])).
% 3.04/3.25 tff(13638,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13639,plain,
% 3.04/3.25 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13638, 13635, 12045, 13611, 13530])).
% 3.04/3.25 tff(13640,plain,
% 3.04/3.25 (r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[9958, 13639])).
% 3.04/3.25 tff(13641,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13642,plain,
% 3.04/3.25 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13643,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[13642])).
% 3.04/3.25 tff(13644,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[13643, 13641])).
% 3.04/3.25 tff(13645,plain,
% 3.04/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(13646,plain,
% 3.04/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[13645, 13644])).
% 3.04/3.25 tff(13647,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13646, 106, 12045, 13611, 13640, 13586])).
% 3.04/3.25 tff(13648,plain,((~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13649,plain,
% 3.04/3.25 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13648, 3686, 2])).
% 3.04/3.25 tff(13650,plain,
% 3.04/3.25 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[225, 13649])).
% 3.04/3.25 tff(13651,plain,
% 3.04/3.25 (~r(s(z), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[10894, 396, 11997, 2])).
% 3.04/3.25 tff(13652,plain,
% 3.04/3.25 (b(s(z), s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[550, 13651])).
% 3.04/3.25 tff(13653,plain,
% 3.04/3.25 (~b(z, s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[11329, 1, 13652])).
% 3.04/3.25 tff(13654,plain,
% 3.04/3.25 (r(z, s(s(z)))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[124, 13653])).
% 3.04/3.25 tff(13655,plain,
% 3.04/3.25 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[6042, 106, 2, 13654, 396])).
% 3.04/3.25 tff(13656,plain,
% 3.04/3.25 (b(z, s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[498, 13655])).
% 3.04/3.25 tff(13657,plain,
% 3.04/3.25 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[6027, 106, 2, 13654, 396])).
% 3.04/3.25 tff(13658,plain,
% 3.04/3.25 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[145, 13657])).
% 3.04/3.25 tff(13659,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[11680, 171, 13652, 1, 9835, 13658, 13656])).
% 3.04/3.25 tff(13660,plain,((~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13661,plain,
% 3.04/3.25 (~b(s(s(z)), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13660, 13650, 2])).
% 3.04/3.25 tff(13662,plain,
% 3.04/3.25 (r(s(s(z)), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[157, 13661])).
% 3.04/3.25 tff(13663,plain,
% 3.04/3.25 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[959, 13662, 13459, 13650])).
% 3.04/3.25 tff(13664,plain,
% 3.04/3.25 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[145, 13663])).
% 3.04/3.25 tff(13665,plain,
% 3.04/3.25 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13605, 2828, 13481, 6477])).
% 3.04/3.25 tff(13666,plain,
% 3.04/3.25 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1368, 13665])).
% 3.04/3.25 tff(13667,plain,
% 3.04/3.25 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[10752, 13666, 10693, 3686, 376])).
% 3.04/3.25 tff(13668,plain,
% 3.04/3.25 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[2614, 13667])).
% 3.04/3.25 tff(13669,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13670,plain,
% 3.04/3.25 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13671,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[13670])).
% 3.04/3.25 tff(13672,plain,
% 3.04/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(transitivity,[status(thm)],[13671, 13669])).
% 3.04/3.25 tff(13673,plain,
% 3.04/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(13674,plain,
% 3.04/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[13673, 13672])).
% 3.04/3.25 tff(13675,plain,
% 3.04/3.25 ($false),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13674, 106, 13481, 13668, 6477, 2828])).
% 3.04/3.25 tff(13676,plain,((~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)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.25 tff(13677,plain,
% 3.04/3.25 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13676, 6477, 3686, 376])).
% 3.04/3.25 tff(13678,plain,
% 3.04/3.25 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[10361, 13677])).
% 3.04/3.25 tff(13679,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13680,plain,
% 3.04/3.25 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13681,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 3.04/3.25 inference(monotonicity,[status(thm)],[13680])).
% 3.04/3.25 tff(13682,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.25 inference(transitivity,[status(thm)],[13681, 13679])).
% 3.04/3.25 tff(13683,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(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))))),
% 3.04/3.25 inference(quant_inst,[status(thm)],[])).
% 3.04/3.25 tff(13684,plain,
% 3.04/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.04/3.25 inference(modus_ponens,[status(thm)],[13683, 13682])).
% 3.04/3.25 tff(13685,plain,
% 3.04/3.25 (~b(s(s(s(z))), s(z))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[13684, 171, 9835, 3686, 376, 13678, 159])).
% 3.04/3.25 tff(13686,plain,
% 3.04/3.25 (r(s(s(s(z))), s(z))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1173, 13685])).
% 3.04/3.25 tff(13687,plain,
% 3.04/3.25 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[8843, 13686, 13481, 6477])).
% 3.04/3.25 tff(13688,plain,
% 3.04/3.25 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.25 inference(unit_resolution,[status(thm)],[1368, 13687])).
% 3.04/3.25 tff(13689,plain,
% 3.04/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.25 inference(rewrite,[status(thm)],[])).
% 3.04/3.25 tff(13690,plain,
% 3.04/3.25 (((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13691,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[13690])).
% 3.04/3.26 tff(13692,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.26 inference(transitivity,[status(thm)],[13691, 13689])).
% 3.04/3.26 tff(13693,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(13694,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[13693, 13692])).
% 3.04/3.26 tff(13695,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13694, 171, 9835, 10693, 1384, 159, 1313])).
% 3.04/3.26 tff(13696,plain,((~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(13697,plain,
% 3.04/3.26 (~b(z, s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13696, 13688, 159])).
% 3.04/3.26 tff(13698,plain,
% 3.04/3.26 (r(z, s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[498, 13697])).
% 3.04/3.26 tff(13699,plain,
% 3.04/3.26 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10752, 13688, 10693, 3686, 376])).
% 3.04/3.26 tff(13700,plain,
% 3.04/3.26 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2614, 13699])).
% 3.04/3.26 tff(13701,plain,
% 3.04/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13702,plain,
% 3.04/3.26 (((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~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(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13703,plain,
% 3.04/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[13702])).
% 3.04/3.26 tff(13704,plain,
% 3.04/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[13703, 13701])).
% 3.04/3.26 tff(13705,plain,
% 3.04/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(13706,plain,
% 3.04/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[13705, 13704])).
% 3.04/3.26 tff(13707,plain,
% 3.04/3.26 (~r(z, s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13706, 106, 13481, 13700, 13698])).
% 3.04/3.26 tff(13708,plain,
% 3.04/3.26 (b(z, s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[9192, 13707])).
% 3.04/3.26 tff(13709,plain,
% 3.04/3.26 (~r(s(s(s(z))), z)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[8736, 106, 13481, 13700, 13698])).
% 3.04/3.26 tff(13710,plain,
% 3.04/3.26 (b(s(s(s(z))), z)),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10429, 13709])).
% 3.04/3.26 tff(13711,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13712,plain,
% 3.04/3.26 (((~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(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13713,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[13712])).
% 3.04/3.26 tff(13714,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[13713, 13711])).
% 3.04/3.26 tff(13715,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(13716,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[13715, 13714])).
% 3.04/3.26 tff(13717,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13716, 171, 9835, 11701, 13678, 13710, 13708])).
% 3.04/3.26 tff(13718,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(13719,plain,
% 3.04/3.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13718, 13664, 3686, 12043])).
% 3.04/3.26 tff(13720,plain,
% 3.04/3.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[6475, 13719])).
% 3.04/3.26 tff(13721,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13722,plain,
% 3.04/3.26 (((~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(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13723,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[13722])).
% 3.04/3.26 tff(13724,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(transitivity,[status(thm)],[13723, 13721])).
% 3.04/3.26 tff(13725,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(13726,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[13725, 13724])).
% 3.04/3.26 tff(13727,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13726, 171, 3686, 11701, 376, 6462, 2852])).
% 3.04/3.26 tff(13728,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(13729,plain,
% 3.04/3.26 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13728, 3686, 12043, 13720])).
% 3.04/3.26 tff(13730,plain,
% 3.04/3.26 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10361, 13729])).
% 3.04/3.26 tff(13731,plain,
% 3.04/3.26 (~r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[12068, 2828, 13481, 263])).
% 3.04/3.26 tff(13732,plain,
% 3.04/3.26 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[1368, 13731])).
% 3.04/3.26 tff(13733,plain,
% 3.04/3.26 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10752, 13732, 10693, 3686, 376])).
% 3.04/3.26 tff(13734,plain,
% 3.04/3.26 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2614, 13733])).
% 3.04/3.26 tff(13735,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[12524, 106, 13481, 13734, 263, 2828])).
% 3.04/3.26 tff(13736,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(13737,plain,
% 3.04/3.26 (~r(s(s(s(s(z)))), s(z))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13736, 13730, 3686, 12043])).
% 3.04/3.26 tff(13738,plain,
% 3.04/3.26 (b(s(s(s(s(z)))), s(z))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[9955, 13737])).
% 3.04/3.26 tff(13739,plain,
% 3.04/3.26 (~b(z, s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[8932, 13738, 10693, 3686, 13664])).
% 3.04/3.26 tff(13740,plain,
% 3.04/3.26 (r(z, s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[498, 13739])).
% 3.04/3.26 tff(13741,plain,
% 3.04/3.26 (~r(z, s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[11648, 13740, 13650, 13662])).
% 3.04/3.26 tff(13742,plain,
% 3.04/3.26 (b(z, s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[124, 13741])).
% 3.04/3.26 tff(13743,plain,
% 3.04/3.26 (~r(s(z), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10894, 13650, 11997, 2])).
% 3.04/3.26 tff(13744,plain,
% 3.04/3.26 (b(s(z), s(s(z)))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[550, 13743])).
% 3.04/3.26 tff(13745,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13746,plain,
% 3.04/3.26 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13747,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))))),
% 3.04/3.26 inference(monotonicity,[status(thm)],[13746])).
% 3.04/3.26 tff(13748,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.04/3.26 inference(transitivity,[status(thm)],[13747, 13745])).
% 3.04/3.26 tff(13749,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(z))))),
% 3.04/3.26 inference(quant_inst,[status(thm)],[])).
% 3.04/3.26 tff(13750,plain,
% 3.04/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.04/3.26 inference(modus_ponens,[status(thm)],[13749, 13748])).
% 3.04/3.26 tff(13751,plain,
% 3.04/3.26 ($false),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13750, 171, 13744, 13742, 3686, 10693, 13664, 13738])).
% 3.04/3.26 tff(13752,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.26 tff(13753,plain,
% 3.04/3.26 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[13752, 2])).
% 3.04/3.26 tff(13754,plain,
% 3.04/3.26 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[3668, 13753])).
% 3.04/3.26 tff(13755,plain,
% 3.04/3.26 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[8446, 1384, 10693, 11701])).
% 3.04/3.26 tff(13756,plain,
% 3.04/3.26 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[2614, 13755])).
% 3.04/3.26 tff(13757,plain,
% 3.04/3.26 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[8535, 13756, 502, 260])).
% 3.04/3.26 tff(13758,plain,
% 3.04/3.26 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[10361, 13757])).
% 3.04/3.26 tff(13759,plain,
% 3.04/3.26 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[9195, 13756, 502, 260])).
% 3.04/3.26 tff(13760,plain,
% 3.04/3.26 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.26 inference(unit_resolution,[status(thm)],[6475, 13759])).
% 3.04/3.26 tff(13761,plain,
% 3.04/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.26 inference(rewrite,[status(thm)],[])).
% 3.04/3.26 tff(13762,plain,
% 3.04/3.26 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13763,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13762])).
% 3.04/3.27 tff(13764,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[13763, 13761])).
% 3.04/3.27 tff(13765,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(13766,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z)))))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[13765, 13764])).
% 3.04/3.27 tff(13767,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13766, 171, 11701, 10693, 1384, 13760, 13758])).
% 3.04/3.27 tff(13768,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(13769,plain,
% 3.04/3.27 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13768, 11997, 13754])).
% 3.04/3.27 tff(13770,plain,
% 3.04/3.27 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1368, 13769])).
% 3.04/3.27 tff(13771,plain,
% 3.04/3.27 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[11961, 13770, 12043, 13754])).
% 3.04/3.27 tff(13772,plain,
% 3.04/3.27 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[2614, 13771])).
% 3.04/3.27 tff(13773,plain,
% 3.04/3.27 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[8446, 1384, 10693, 1976])).
% 3.04/3.27 tff(13774,plain,
% 3.04/3.27 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[2614, 13773])).
% 3.04/3.27 tff(13775,plain,
% 3.04/3.27 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[8535, 13774, 502, 260])).
% 3.04/3.27 tff(13776,plain,
% 3.04/3.27 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[10361, 13775])).
% 3.04/3.27 tff(13777,plain,
% 3.04/3.27 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[9195, 13774, 502, 260])).
% 3.04/3.27 tff(13778,plain,
% 3.04/3.27 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[6475, 13777])).
% 3.04/3.27 tff(13779,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[8628, 171, 83, 1384, 13778, 13776])).
% 3.04/3.27 tff(13780,plain,((~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(13781,plain,
% 3.04/3.27 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13780, 83, 11701, 11997, 13754])).
% 3.04/3.27 tff(13782,plain,
% 3.04/3.27 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[1368, 13781])).
% 3.04/3.27 tff(13783,plain,
% 3.04/3.27 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[11961, 13782, 12043, 13754])).
% 3.04/3.27 tff(13784,plain,
% 3.04/3.27 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[2614, 13783])).
% 3.04/3.27 tff(13785,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13786,plain,
% 3.04/3.27 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13787,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13786])).
% 3.04/3.27 tff(13788,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[13787, 13785])).
% 3.04/3.27 tff(13789,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(13790,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[13789, 13788])).
% 3.04/3.27 tff(13791,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13790, 171, 9835, 11701, 838, 11979, 11971])).
% 3.04/3.27 tff(13792,plain,((~r(z, s(s(s(s(z)))))) | (~b(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(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(13793,plain,
% 3.04/3.27 (~r(z, s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13792, 2828, 13754, 13784])).
% 3.04/3.27 tff(13794,plain,
% 3.04/3.27 (b(z, s(s(s(s(z)))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[293, 13793])).
% 3.04/3.27 tff(13795,plain,
% 3.04/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13796,plain,
% 3.04/3.27 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13797,plain,
% 3.04/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13796])).
% 3.04/3.27 tff(13798,plain,
% 3.04/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[13797, 13795])).
% 3.04/3.27 tff(13799,plain,
% 3.04/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(13800,plain,
% 3.04/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[13799, 13798])).
% 3.04/3.27 tff(13801,plain,
% 3.04/3.27 ($false),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13800, 106, 260, 1357, 6477, 2828])).
% 3.04/3.27 tff(13802,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.27 tff(13803,plain,
% 3.04/3.27 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13802, 2828, 13782, 13754])).
% 3.04/3.27 tff(13804,plain,
% 3.04/3.27 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[6475, 13803])).
% 3.04/3.27 tff(13805,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13806,plain,
% 3.04/3.27 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13807,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13806])).
% 3.04/3.27 tff(13808,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[13807, 13805])).
% 3.04/3.27 tff(13809,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(z))))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(13810,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[13809, 13808])).
% 3.04/3.27 tff(13811,plain,
% 3.04/3.27 (~b(z, s(z))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13810, 171, 13784, 10693, 12043, 13804, 13794])).
% 3.04/3.27 tff(13812,plain,
% 3.04/3.27 (r(z, s(z))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[93, 13811])).
% 3.04/3.27 tff(13813,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13814,plain,
% 3.04/3.27 (((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13815,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13814])).
% 3.04/3.27 tff(13816,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))))),
% 3.04/3.27 inference(transitivity,[status(thm)],[13815, 13813])).
% 3.04/3.27 tff(13817,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), z)))),
% 3.04/3.27 inference(quant_inst,[status(thm)],[])).
% 3.04/3.27 tff(13818,plain,
% 3.04/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 3.04/3.27 inference(modus_ponens,[status(thm)],[13817, 13816])).
% 3.04/3.27 tff(13819,plain,
% 3.04/3.27 (~b(z, s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[13818, 171, 9835, 11701, 83, 13784, 13794])).
% 3.04/3.27 tff(13820,plain,
% 3.04/3.27 (r(z, s(s(s(z))))),
% 3.04/3.27 inference(unit_resolution,[status(thm)],[9192, 13819])).
% 3.04/3.27 tff(13821,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(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)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(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)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13822,plain,
% 3.04/3.27 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.27 inference(rewrite,[status(thm)],[])).
% 3.04/3.27 tff(13823,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(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))))))))),
% 3.04/3.27 inference(monotonicity,[status(thm)],[13822])).
% 3.04/3.27 tff(13824,plain,
% 3.04/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(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)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13823, 13821])).
% 3.04/3.28 tff(13825,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13826,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(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))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[13825, 13824])).
% 3.04/3.28 tff(13827,plain,
% 3.04/3.28 (~b(s(s(s(z))), s(z))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13826, 171, 11701, 83, 13784, 10693, 13804])).
% 3.04/3.28 tff(13828,plain,
% 3.04/3.28 (r(s(s(s(z))), s(z))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[1173, 13827])).
% 3.04/3.28 tff(13829,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13830,plain,
% 3.04/3.28 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13831,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[13830])).
% 3.04/3.28 tff(13832,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13831, 13829])).
% 3.04/3.28 tff(13833,plain,
% 3.04/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13834,plain,
% 3.04/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[13833, 13832])).
% 3.04/3.28 tff(13835,plain,
% 3.04/3.28 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13834, 106, 13782, 13828, 13820])).
% 3.04/3.28 tff(13836,plain,
% 3.04/3.28 (b(z, s(s(s(s(s(z))))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[498, 13835])).
% 3.04/3.28 tff(13837,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13838,plain,
% 3.04/3.28 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(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(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13839,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[13838])).
% 3.04/3.28 tff(13840,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, 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(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13839, 13837])).
% 3.04/3.28 tff(13841,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13842,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[13841, 13840])).
% 3.04/3.28 tff(13843,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13842, 171, 83, 356, 1313, 2527, 2352])).
% 3.04/3.28 tff(13844,plain,((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13845,plain,
% 3.04/3.28 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13844, 356, 83, 1313, 2527])).
% 3.04/3.28 tff(13846,plain,
% 3.04/3.28 (r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[351, 13845])).
% 3.04/3.28 tff(13847,plain,
% 3.04/3.28 (~r(s(s(s(s(z)))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[11880, 13846, 637, 96])).
% 3.04/3.28 tff(13848,plain,
% 3.04/3.28 (b(s(s(s(s(z)))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[274, 13847])).
% 3.04/3.28 tff(13849,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13850,plain,
% 3.04/3.28 (((~b(s(s(s(s(z)))), 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(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13851,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[13850])).
% 3.04/3.28 tff(13852,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13851, 13849])).
% 3.04/3.28 tff(13853,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(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)))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13854,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[13853, 13852])).
% 3.04/3.28 tff(13855,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13854, 171, 9835, 376, 356, 2527, 13848])).
% 3.04/3.28 tff(13856,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13857,plain,
% 3.04/3.28 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13856, 2527, 376, 637, 96, 83, 1313])).
% 3.04/3.28 tff(13858,plain,
% 3.04/3.28 (r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[9958, 13857])).
% 3.04/3.28 tff(13859,plain,
% 3.04/3.28 (~r(s(s(s(s(z)))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[6904, 13858, 96, 637])).
% 3.04/3.28 tff(13860,plain,
% 3.04/3.28 (b(s(s(s(s(z)))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[274, 13859])).
% 3.04/3.28 tff(13861,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[8065, 171, 83, 1313, 2527, 13860])).
% 3.04/3.28 tff(13862,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(z))))))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13863,plain,
% 3.04/3.28 (~r(s(s(z)), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13862, 13836, 83, 13794, 13812, 12043])).
% 3.04/3.28 tff(13864,plain,
% 3.04/3.28 (b(s(s(z)), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[157, 13863])).
% 3.04/3.28 tff(13865,plain,
% 3.04/3.28 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13660, 13864, 2])).
% 3.04/3.28 tff(13866,plain,
% 3.04/3.28 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[10522, 13820, 13828, 13782])).
% 3.04/3.28 tff(13867,plain,
% 3.04/3.28 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[145, 13866])).
% 3.04/3.28 tff(13868,plain,
% 3.04/3.28 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[6961, 13864, 13836, 13867])).
% 3.04/3.28 tff(13869,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[225, 13868, 13865])).
% 3.04/3.28 tff(13870,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13871,plain,
% 3.04/3.28 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13870, 83, 2])).
% 3.04/3.28 tff(13872,plain,
% 3.04/3.28 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[10361, 13871])).
% 3.04/3.28 tff(13873,plain,
% 3.04/3.28 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[8853, 13872, 12043, 13784, 11701])).
% 3.04/3.28 tff(13874,plain,
% 3.04/3.28 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[6475, 13873])).
% 3.04/3.28 tff(13875,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13876,plain,
% 3.04/3.28 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13877,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[13876])).
% 3.04/3.28 tff(13878,plain,
% 3.04/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z)))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13877, 13875])).
% 3.04/3.28 tff(13879,plain,
% 3.04/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13880,plain,
% 3.04/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(z))), z))),
% 3.04/3.28 inference(modus_ponens,[status(thm)],[13879, 13878])).
% 3.04/3.28 tff(13881,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13880, 106, 260, 1357, 6477, 10561])).
% 3.04/3.28 tff(13882,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13883,plain,
% 3.04/3.28 (~r(s(s(s(z))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13882, 13782, 13754, 13874])).
% 3.04/3.28 tff(13884,plain,
% 3.04/3.28 (b(s(s(s(z))), z)),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[10429, 13883])).
% 3.04/3.28 tff(13885,plain,
% 3.04/3.28 ($false),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13790, 171, 9835, 11701, 838, 1091, 9277])).
% 3.04/3.28 tff(13886,plain,((~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.28 tff(13887,plain,
% 3.04/3.28 (~b(z, s(s(s(z))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[13886, 13784, 13884])).
% 3.04/3.28 tff(13888,plain,
% 3.04/3.28 (r(z, s(s(s(z))))),
% 3.04/3.28 inference(unit_resolution,[status(thm)],[9192, 13887])).
% 3.04/3.28 tff(13889,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13890,plain,
% 3.04/3.28 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), 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(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 3.04/3.28 inference(rewrite,[status(thm)],[])).
% 3.04/3.28 tff(13891,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 3.04/3.28 inference(monotonicity,[status(thm)],[13890])).
% 3.04/3.28 tff(13892,plain,
% 3.04/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 3.04/3.28 inference(transitivity,[status(thm)],[13891, 13889])).
% 3.04/3.28 tff(13893,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(z))))))),
% 3.04/3.28 inference(quant_inst,[status(thm)],[])).
% 3.04/3.28 tff(13894,plain,
% 3.04/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13893, 13892])).
% 3.04/3.29 tff(13895,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13894, 171, 11701, 83, 838, 10693, 1091, 2141])).
% 3.04/3.29 tff(13896,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13897,plain,
% 3.04/3.29 (~b(s(s(s(s(z)))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13896, 83, 13784, 13884])).
% 3.04/3.29 tff(13898,plain,
% 3.04/3.29 (r(s(s(s(s(z)))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[274, 13897])).
% 3.04/3.29 tff(13899,plain,
% 3.04/3.29 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13660, 1, 2])).
% 3.04/3.29 tff(13900,plain,
% 3.04/3.29 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[225, 13899])).
% 3.04/3.29 tff(13901,plain,
% 3.04/3.29 (~r(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9352, 554, 11997, 2])).
% 3.04/3.29 tff(13902,plain,
% 3.04/3.29 (b(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1173, 13901])).
% 3.04/3.29 tff(13903,plain,
% 3.04/3.29 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[12035, 13902, 13784, 207])).
% 3.04/3.29 tff(13904,plain,
% 3.04/3.29 (r(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[205, 13903])).
% 3.04/3.29 tff(13905,plain,
% 3.04/3.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[510, 13904, 11997, 13754])).
% 3.04/3.29 tff(13906,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[351, 13905])).
% 3.04/3.29 tff(13907,plain,
% 3.04/3.29 (~b(s(s(s(s(z)))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13584, 13872, 12043])).
% 3.04/3.29 tff(13908,plain,
% 3.04/3.29 (r(s(s(s(s(z)))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9955, 13907])).
% 3.04/3.29 tff(13909,plain,
% 3.04/3.29 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[8149, 13904, 554, 13908])).
% 3.04/3.29 tff(13910,plain,
% 3.04/3.29 (b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9958, 13909])).
% 3.04/3.29 tff(13911,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[11946, 13910, 13906, 83, 207])).
% 3.04/3.29 tff(13912,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13913,plain,
% 3.04/3.29 (~r(s(z), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13912, 13900, 83, 2])).
% 3.04/3.29 tff(13914,plain,
% 3.04/3.29 (b(s(z), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[550, 13913])).
% 3.04/3.29 tff(13915,plain,
% 3.04/3.29 (~b(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10237, 13914, 1])).
% 3.04/3.29 tff(13916,plain,
% 3.04/3.29 (r(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[93, 13915])).
% 3.04/3.29 tff(13917,plain,
% 3.04/3.29 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[11320, 13916, 13754, 1, 13914, 13782])).
% 3.04/3.29 tff(13918,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[205, 13917])).
% 3.04/3.29 tff(13919,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13920,plain,
% 3.04/3.29 (((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(z), 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(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13921,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[13920])).
% 3.04/3.29 tff(13922,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), 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(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[13921, 13919])).
% 3.04/3.29 tff(13923,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(13924,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13923, 13922])).
% 3.04/3.29 tff(13925,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13924, 171, 13914, 83, 10693, 13918, 13900])).
% 3.04/3.29 tff(13926,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13927,plain,
% 3.04/3.29 (~b(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13926, 83, 2])).
% 3.04/3.29 tff(13928,plain,
% 3.04/3.29 (r(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[157, 13927])).
% 3.04/3.29 tff(13929,plain,
% 3.04/3.29 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[11880, 2118, 637, 96])).
% 3.04/3.29 tff(13930,plain,
% 3.04/3.29 (b(s(s(z)), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[351, 13929])).
% 3.04/3.29 tff(13931,plain,
% 3.04/3.29 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[6904, 2118, 637, 96])).
% 3.04/3.29 tff(13932,plain,
% 3.04/3.29 (b(s(s(s(s(z)))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9958, 13931])).
% 3.04/3.29 tff(13933,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13934,plain,
% 3.04/3.29 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(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(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13935,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[13934])).
% 3.04/3.29 tff(13936,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[13935, 13933])).
% 3.04/3.29 tff(13937,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(13938,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13937, 13936])).
% 3.04/3.29 tff(13939,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13938, 171, 83, 10693, 376, 13932, 13930])).
% 3.04/3.29 tff(13940,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13941,plain,
% 3.04/3.29 (~r(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13940, 13928, 12043, 83, 13898])).
% 3.04/3.29 tff(13942,plain,
% 3.04/3.29 (b(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[93, 13941])).
% 3.04/3.29 tff(13943,plain,
% 3.04/3.29 (~b(s(s(s(s(s(z))))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10694, 13942, 10693])).
% 3.04/3.29 tff(13944,plain,
% 3.04/3.29 (r(s(s(s(s(s(z))))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[145, 13943])).
% 3.04/3.29 tff(13945,plain,
% 3.04/3.29 (~b(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10424, 13942, 13884])).
% 3.04/3.29 tff(13946,plain,
% 3.04/3.29 (r(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1173, 13945])).
% 3.04/3.29 tff(13947,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10522, 13946, 13944, 13888, 13782])).
% 3.04/3.29 tff(13948,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13949,plain,
% 3.04/3.29 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13948, 2])).
% 3.04/3.29 tff(13950,plain,
% 3.04/3.29 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[427, 13949])).
% 3.04/3.29 tff(13951,plain,
% 3.04/3.29 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[8834, 13770, 13754, 13950])).
% 3.04/3.29 tff(13952,plain,
% 3.04/3.29 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10361, 13951])).
% 3.04/3.29 tff(13953,plain,
% 3.04/3.29 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[8853, 13952, 12043, 13772, 11701])).
% 3.04/3.29 tff(13954,plain,
% 3.04/3.29 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[6475, 13953])).
% 3.04/3.29 tff(13955,plain,
% 3.04/3.29 (~r(s(s(s(z))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13882, 13954, 13754, 13770])).
% 3.04/3.29 tff(13956,plain,
% 3.04/3.29 (b(s(s(s(z))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10429, 13955])).
% 3.04/3.29 tff(13957,plain,
% 3.04/3.29 (~r(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[8843, 13954, 13950, 13770])).
% 3.04/3.29 tff(13958,plain,
% 3.04/3.29 (b(s(s(s(z))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[1173, 13957])).
% 3.04/3.29 tff(13959,plain,
% 3.04/3.29 (~b(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[10424, 13958, 13956])).
% 3.04/3.29 tff(13960,plain,
% 3.04/3.29 (r(z, s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[93, 13959])).
% 3.04/3.29 tff(13961,plain,
% 3.04/3.29 (~b(s(s(s(s(z)))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13584, 13952, 12043])).
% 3.04/3.29 tff(13962,plain,
% 3.04/3.29 (r(s(s(s(s(z)))), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9955, 13961])).
% 3.04/3.29 tff(13963,plain,
% 3.04/3.29 (~b(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13660, 396, 2])).
% 3.04/3.29 tff(13964,plain,
% 3.04/3.29 (r(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[157, 13963])).
% 3.04/3.29 tff(13965,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13966,plain,
% 3.04/3.29 (((~b(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(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13967,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[13966])).
% 3.04/3.29 tff(13968,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[13967, 13965])).
% 3.04/3.29 tff(13969,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(z), z)))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(13970,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13969, 13968])).
% 3.04/3.29 tff(13971,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13970, 171, 9835, 376, 13615, 2527, 13613])).
% 3.04/3.29 tff(13972,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13973,plain,
% 3.04/3.29 (~r(s(s(s(s(z)))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13972, 2527, 376, 96, 637])).
% 3.04/3.29 tff(13974,plain,
% 3.04/3.29 (b(s(s(s(s(z)))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[274, 13973])).
% 3.04/3.29 tff(13975,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13526, 171, 9835, 376, 2527, 13974])).
% 3.04/3.29 tff(13976,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13977,plain,
% 3.04/3.29 (~b(z, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13976, 13964, 13960, 12043])).
% 3.04/3.29 tff(13978,plain,
% 3.04/3.29 (r(z, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[293, 13977])).
% 3.04/3.29 tff(13979,plain,
% 3.04/3.29 (((~r(s(s(s(s(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(z)))))) | (~r(z, s(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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13980,plain,
% 3.04/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[13979])).
% 3.04/3.29 tff(13981,plain,
% 3.04/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z)))))))),
% 3.04/3.29 inference(transitivity,[status(thm)],[13980, 8717])).
% 3.04/3.29 tff(13982,plain,
% 3.04/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(13983,plain,
% 3.04/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~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(z))))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(s(z))))))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13982, 13981])).
% 3.04/3.29 tff(13984,plain,
% 3.04/3.29 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13983, 106, 13754, 13950, 13978])).
% 3.04/3.29 tff(13985,plain,
% 3.04/3.29 (b(z, s(s(s(s(s(z))))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[498, 13984])).
% 3.04/3.29 tff(13986,plain,
% 3.04/3.29 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[959, 13964, 13960, 396])).
% 3.04/3.29 tff(13987,plain,
% 3.04/3.29 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[145, 13986])).
% 3.04/3.29 tff(13988,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13989,plain,
% 3.04/3.29 (((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 3.04/3.29 inference(rewrite,[status(thm)],[])).
% 3.04/3.29 tff(13990,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))))),
% 3.04/3.29 inference(monotonicity,[status(thm)],[13989])).
% 3.04/3.29 tff(13991,plain,
% 3.04/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z)))),
% 3.04/3.29 inference(transitivity,[status(thm)],[13990, 13988])).
% 3.04/3.29 tff(13992,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(z))))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 3.04/3.29 inference(quant_inst,[status(thm)],[])).
% 3.04/3.29 tff(13993,plain,
% 3.04/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(z))), z))),
% 3.04/3.29 inference(modus_ponens,[status(thm)],[13992, 13991])).
% 3.04/3.29 tff(13994,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13993, 171, 9835, 13958, 13987, 13956, 13985])).
% 3.04/3.29 tff(13995,plain,((~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(13996,plain,
% 3.04/3.29 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13995, 2])).
% 3.04/3.29 tff(13997,plain,
% 3.04/3.29 (b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[225, 13996])).
% 3.04/3.29 tff(13998,plain,
% 3.04/3.29 (~b(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13497, 13997, 13950, 13772, 12043, 13962])).
% 3.04/3.29 tff(13999,plain,
% 3.04/3.29 (r(s(s(z)), z)),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[157, 13998])).
% 3.04/3.29 tff(14000,plain,
% 3.04/3.29 (~r(z, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13560, 13997, 13950, 13954, 13962])).
% 3.04/3.29 tff(14001,plain,
% 3.04/3.29 (b(z, s(s(s(s(z)))))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[293, 14000])).
% 3.04/3.29 tff(14002,plain,
% 3.04/3.29 ($false),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[13976, 14001, 13999, 13960, 12043])).
% 3.04/3.29 tff(14003,plain,(~r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.29 tff(14004,plain,
% 3.04/3.29 (b(s(s(z)), s(z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[244, 14003])).
% 3.04/3.29 tff(14005,plain,
% 3.04/3.29 ((~b(z, s(s(z)))) | (~b(s(s(z)), z))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[9982, 14004])).
% 3.04/3.29 tff(14006,plain,
% 3.04/3.29 (~b(z, s(s(z)))),
% 3.04/3.29 inference(unit_resolution,[status(thm)],[14005, 1])).
% 3.04/3.30 tff(14007,plain,
% 3.04/3.30 (r(z, s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[124, 14006])).
% 3.04/3.30 tff(14008,plain,
% 3.04/3.30 (~b(s(z), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[10237, 3281, 1])).
% 3.04/3.30 tff(14009,plain,
% 3.04/3.30 (r(s(z), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[550, 14008])).
% 3.04/3.30 tff(14010,plain,
% 3.04/3.30 (~b(s(s(s(s(s(z))))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11725, 3281])).
% 3.04/3.30 tff(14011,plain,
% 3.04/3.30 (r(s(s(s(s(s(z))))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[479, 14010])).
% 3.04/3.30 tff(14012,plain,
% 3.04/3.30 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[10658, 14004])).
% 3.04/3.30 tff(14013,plain,
% 3.04/3.30 (~b(s(s(s(s(z)))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[14012, 3281])).
% 3.04/3.30 tff(14014,plain,
% 3.04/3.30 (r(s(s(s(s(z)))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[9955, 14013])).
% 3.04/3.30 tff(14015,plain,
% 3.04/3.30 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[7054, 14014, 14011, 14009])).
% 3.04/3.30 tff(14016,plain,
% 3.04/3.30 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[427, 14015])).
% 3.04/3.30 tff(14017,plain,
% 3.04/3.30 ((~b(z, s(z))) | (~b(s(s(s(z))), s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[8284, 11701, 14004])).
% 3.04/3.30 tff(14018,plain,
% 3.04/3.30 (~b(s(s(s(z))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[14017, 3281])).
% 3.04/3.30 tff(14019,plain,
% 3.04/3.30 (r(s(s(s(z))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[1173, 14018])).
% 3.04/3.30 tff(14020,plain,
% 3.04/3.30 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[8249, 14019, 3, 14011])).
% 3.04/3.30 tff(14021,plain,
% 3.04/3.30 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[8203, 14014, 3, 14011])).
% 3.04/3.30 tff(14022,plain,
% 3.04/3.30 ($false),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[3668, 14021, 14020])).
% 3.04/3.30 tff(14023,plain,((~b(z, s(z))) | (~r(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.04/3.30 tff(14024,plain,
% 3.04/3.30 (~b(z, s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[14023, 3])).
% 3.04/3.30 tff(14025,plain,
% 3.04/3.30 (r(z, s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[93, 14024])).
% 3.04/3.30 tff(14026,plain,
% 3.04/3.30 (~r(s(s(s(s(s(z))))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11572, 14025, 3])).
% 3.04/3.30 tff(14027,plain,
% 3.04/3.30 (b(s(s(s(s(s(z))))), s(z))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[479, 14026])).
% 3.04/3.30 tff(14028,plain,
% 3.04/3.30 (~b(s(s(z)), z)),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11508, 14027, 14025])).
% 3.04/3.30 tff(14029,plain,
% 3.04/3.30 (r(s(s(z)), z)),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[157, 14028])).
% 3.04/3.30 tff(14030,plain,
% 3.04/3.30 ((~r(s(z), s(s(z)))) | (~r(z, s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11546, 14004])).
% 3.04/3.30 tff(14031,plain,
% 3.04/3.30 (~r(s(z), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[14030, 14025])).
% 3.04/3.30 tff(14032,plain,
% 3.04/3.30 (b(s(z), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[550, 14031])).
% 3.04/3.30 tff(14033,plain,
% 3.04/3.30 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[471, 171, 14032, 14004, 14027])).
% 3.04/3.30 tff(14034,plain,
% 3.04/3.30 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[225, 14033])).
% 3.04/3.30 tff(14035,plain,
% 3.04/3.30 (~r(s(s(s(s(s(z))))), z)),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[959, 14034, 14025, 14029])).
% 3.04/3.30 tff(14036,plain,
% 3.04/3.30 (b(s(s(s(s(s(z))))), z)),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[145, 14035])).
% 3.04/3.30 tff(14037,plain,
% 3.04/3.30 ((~b(z, s(s(z)))) | (~b(s(z), s(s(z))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11602, 14004])).
% 3.04/3.30 tff(14038,plain,
% 3.04/3.30 (~b(z, s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[14037, 14032])).
% 3.04/3.30 tff(14039,plain,
% 3.04/3.30 (r(z, s(s(z)))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[124, 14038])).
% 3.04/3.30 tff(14040,plain,
% 3.04/3.30 (~r(z, s(s(s(s(s(z))))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11648, 14034, 14039, 14029])).
% 3.04/3.30 tff(14041,plain,
% 3.04/3.30 (b(z, s(s(s(s(s(z))))))),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[498, 14040])).
% 3.04/3.30 tff(14042,plain,
% 3.04/3.30 ($false),
% 3.04/3.30 inference(unit_resolution,[status(thm)],[11840, 14041, 14036, 14027])).
% 3.04/3.30 tff(14043,plain,(~r(s(z), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14044,plain,
% 3.14/3.30 (b(s(z), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9990, 14043])).
% 3.14/3.30 tff(14045,plain,
% 3.14/3.30 ((~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(z), s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[8521, 10693])).
% 3.14/3.30 tff(14046,plain,
% 3.14/3.30 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14045, 14016, 14044])).
% 3.14/3.30 tff(14047,plain,
% 3.14/3.30 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[3668, 14046])).
% 3.14/3.30 tff(14048,plain,
% 3.14/3.30 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[13768, 14047, 14011])).
% 3.14/3.30 tff(14049,plain,
% 3.14/3.30 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1368, 14048])).
% 3.14/3.30 tff(14050,plain,
% 3.14/3.30 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11961, 14049, 14044, 14047])).
% 3.14/3.30 tff(14051,plain,
% 3.14/3.30 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[2614, 14050])).
% 3.14/3.30 tff(14052,plain,
% 3.14/3.30 ((~b(s(s(s(s(s(z))))), z)) | (~b(z, s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[10694, 10693])).
% 3.14/3.30 tff(14053,plain,
% 3.14/3.30 (~b(s(s(s(s(s(z))))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14052, 3281])).
% 3.14/3.30 tff(14054,plain,
% 3.14/3.30 (r(s(s(s(s(s(z))))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[145, 14053])).
% 3.14/3.30 tff(14055,plain,
% 3.14/3.30 (~r(z, s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[10522, 14049, 14019, 14054])).
% 3.14/3.30 tff(14056,plain,
% 3.14/3.30 (b(z, s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9192, 14055])).
% 3.14/3.30 tff(14057,plain,
% 3.14/3.30 ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(z, s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9285, 11701])).
% 3.14/3.30 tff(14058,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14057, 14056, 14051, 14044, 3281, 14016])).
% 3.14/3.30 tff(14059,plain,((~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14060,plain,
% 3.14/3.30 (~b(z, s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14059, 1])).
% 3.14/3.30 tff(14061,plain,
% 3.14/3.30 (r(z, s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[93, 14060])).
% 3.14/3.30 tff(14062,plain,
% 3.14/3.30 (~r(s(z), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14030, 14061])).
% 3.14/3.30 tff(14063,plain,
% 3.14/3.30 (b(s(z), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[550, 14062])).
% 3.14/3.30 tff(14064,plain,
% 3.14/3.30 ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[6253, 14004])).
% 3.14/3.30 tff(14065,plain,
% 3.14/3.30 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14064, 323, 14044])).
% 3.14/3.30 tff(14066,plain,
% 3.14/3.30 (r(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9958, 14065])).
% 3.14/3.30 tff(14067,plain,
% 3.14/3.30 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[10009, 357, 600, 14044, 14066])).
% 3.14/3.30 tff(14068,plain,
% 3.14/3.30 ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[6512, 14004])).
% 3.14/3.30 tff(14069,plain,
% 3.14/3.30 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14068, 357, 323])).
% 3.14/3.30 tff(14070,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[351, 14069, 14067])).
% 3.14/3.30 tff(14071,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14072,plain,
% 3.14/3.30 (~b(s(s(s(s(z)))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14071, 14063, 14007])).
% 3.14/3.30 tff(14073,plain,
% 3.14/3.30 (r(s(s(s(s(z)))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9955, 14072])).
% 3.14/3.30 tff(14074,plain,
% 3.14/3.30 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14064, 14063, 14044])).
% 3.14/3.30 tff(14075,plain,
% 3.14/3.30 (r(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[9958, 14074])).
% 3.14/3.30 tff(14076,plain,
% 3.14/3.30 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14045, 3686, 14044])).
% 3.14/3.30 tff(14077,plain,
% 3.14/3.30 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[427, 14076])).
% 3.14/3.30 tff(14078,plain,
% 3.14/3.30 ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11133, 14004])).
% 3.14/3.30 tff(14079,plain,
% 3.14/3.30 (~b(z, s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14078, 3686, 1])).
% 3.14/3.30 tff(14080,plain,
% 3.14/3.30 (r(z, s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[293, 14079])).
% 3.14/3.30 tff(14081,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11682, 14080, 14077, 1, 14075, 14063, 14073])).
% 3.14/3.30 tff(14082,plain,((~b(s(s(s(s(z)))), s(s(s(s(s(z))))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14083,plain,
% 3.14/3.30 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14082, 1])).
% 3.14/3.30 tff(14084,plain,
% 3.14/3.30 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[3668, 14083])).
% 3.14/3.30 tff(14085,plain,
% 3.14/3.30 (~b(s(s(s(s(s(z))))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11508, 14061, 1])).
% 3.14/3.30 tff(14086,plain,
% 3.14/3.30 (r(s(s(s(s(s(z))))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[479, 14085])).
% 3.14/3.30 tff(14087,plain,
% 3.14/3.30 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[13768, 14084, 14086])).
% 3.14/3.30 tff(14088,plain,
% 3.14/3.30 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1368, 14087])).
% 3.14/3.30 tff(14089,plain,
% 3.14/3.30 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11320, 14088, 1, 14061, 14063, 14084])).
% 3.14/3.30 tff(14090,plain,
% 3.14/3.30 (b(s(s(z)), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[205, 14089])).
% 3.14/3.30 tff(14091,plain,
% 3.14/3.30 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[11961, 14088, 14044, 14084])).
% 3.14/3.30 tff(14092,plain,
% 3.14/3.30 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[2614, 14091])).
% 3.14/3.30 tff(14093,plain,
% 3.14/3.30 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[12068, 5609, 263, 1357])).
% 3.14/3.30 tff(14094,plain,
% 3.14/3.30 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[10361, 14093])).
% 3.14/3.30 tff(14095,plain,
% 3.14/3.30 (~r(s(s(s(z))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[8843, 1357, 5609, 6477])).
% 3.14/3.30 tff(14096,plain,
% 3.14/3.30 (b(s(s(s(z))), s(z))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[1173, 14095])).
% 3.14/3.30 tff(14097,plain,
% 3.14/3.30 (~r(s(s(s(z))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[10763, 1357, 5609, 6477])).
% 3.14/3.30 tff(14098,plain,
% 3.14/3.30 (b(s(s(s(z))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[2642, 14097])).
% 3.14/3.30 tff(14099,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[5518, 14098, 14096, 259, 1976])).
% 3.14/3.30 tff(14100,plain,((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14101,plain,
% 3.14/3.30 ((~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14100, 11701, 14004])).
% 3.14/3.30 tff(14102,plain,
% 3.14/3.30 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14101, 5609, 1357])).
% 3.14/3.30 tff(14103,plain,
% 3.14/3.30 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[6475, 14102])).
% 3.14/3.30 tff(14104,plain,
% 3.14/3.30 ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[8853, 11701])).
% 3.14/3.30 tff(14105,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14104, 14103, 14094, 14044, 838])).
% 3.14/3.30 tff(14106,plain,((~r(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.30 tff(14107,plain,
% 3.14/3.30 (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14106, 14092, 14088, 14073])).
% 3.14/3.30 tff(14108,plain,
% 3.14/3.30 (b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[427, 14107])).
% 3.14/3.30 tff(14109,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), 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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14110,plain,
% 3.14/3.30 (((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(s(z)), 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(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14111,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[14110])).
% 3.14/3.30 tff(14112,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[14111, 14109])).
% 3.14/3.30 tff(14113,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(14114,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z)))))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[14113, 14112])).
% 3.14/3.30 tff(14115,plain,
% 3.14/3.30 (~b(s(s(s(z))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14114, 171, 14063, 14004, 11701, 14092, 10693])).
% 3.14/3.30 tff(14116,plain,
% 3.14/3.30 (r(s(s(s(z))), s(s(z)))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[2642, 14115])).
% 3.14/3.30 tff(14117,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14118,plain,
% 3.14/3.30 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z)))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14119,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[14118])).
% 3.14/3.30 tff(14120,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[14119, 14117])).
% 3.14/3.30 tff(14121,plain,
% 3.14/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(14122,plain,
% 3.14/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(s(s(z))))))) | (~r(z, s(s(s(z)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[14121, 14120])).
% 3.14/3.30 tff(14123,plain,
% 3.14/3.30 (~r(z, s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14122, 106, 14088, 14116, 1975])).
% 3.14/3.30 tff(14124,plain,
% 3.14/3.30 (b(z, s(s(s(s(s(z))))))),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[498, 14123])).
% 3.14/3.30 tff(14125,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14126,plain,
% 3.14/3.30 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14127,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[14126])).
% 3.14/3.30 tff(14128,plain,
% 3.14/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 3.14/3.30 inference(transitivity,[status(thm)],[14127, 14125])).
% 3.14/3.30 tff(14129,plain,
% 3.14/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(s(s(s(s(s(z))))), z)))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(14130,plain,
% 3.14/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[14129, 14128])).
% 3.14/3.30 tff(14131,plain,
% 3.14/3.30 (~r(s(s(s(s(s(z))))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14130, 106, 14088, 14116, 1975])).
% 3.14/3.30 tff(14132,plain,
% 3.14/3.30 (b(s(s(s(s(s(z))))), z)),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[145, 14131])).
% 3.14/3.30 tff(14133,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(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(z)))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14134,plain,
% 3.14/3.30 (((~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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), 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)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.14/3.30 inference(rewrite,[status(thm)],[])).
% 3.14/3.30 tff(14135,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(z))))))) | (~b(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(z)))))) | (~b(s(s(s(s(s(z))))), z))))),
% 3.14/3.30 inference(monotonicity,[status(thm)],[14134])).
% 3.14/3.30 tff(14136,plain,
% 3.14/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(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(z)))))) | (~b(s(s(s(s(s(z))))), z)))),
% 3.14/3.30 inference(transitivity,[status(thm)],[14135, 14133])).
% 3.14/3.30 tff(14137,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, 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(s(z))))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.14/3.30 inference(quant_inst,[status(thm)],[])).
% 3.14/3.30 tff(14138,plain,
% 3.14/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(z))))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), z))),
% 3.14/3.30 inference(modus_ponens,[status(thm)],[14137, 14136])).
% 3.14/3.30 tff(14139,plain,
% 3.14/3.30 ($false),
% 3.14/3.30 inference(unit_resolution,[status(thm)],[14138, 171, 1, 83, 160, 159, 1313])).
% 3.14/3.30 tff(14140,plain,((~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(s(s(s(z))))), z)) | (~b(z, s(s(s(s(s(z)))))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14141,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14140, 14132, 14124, 14108, 1, 14090])).
% 3.14/3.31 tff(14142,plain,((~r(z, s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14143,plain,
% 3.14/3.31 (~r(z, s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14142, 1])).
% 3.14/3.31 tff(14144,plain,
% 3.14/3.31 (b(z, s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[9192, 14143])).
% 3.14/3.31 tff(14145,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(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(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(14146,plain,
% 3.14/3.31 (((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 3.14/3.31 inference(rewrite,[status(thm)],[])).
% 3.14/3.31 tff(14147,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))))),
% 3.14/3.31 inference(monotonicity,[status(thm)],[14146])).
% 3.14/3.31 tff(14148,plain,
% 3.14/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))))),
% 3.14/3.31 inference(transitivity,[status(thm)],[14147, 14145])).
% 3.14/3.31 tff(14149,plain,
% 3.14/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.14/3.31 inference(quant_inst,[status(thm)],[])).
% 3.14/3.31 tff(14150,plain,
% 3.14/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X1, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(s(z))))))) | (~b(s(s(s(z))), s(s(s(s(s(z))))))) | (~b(z, s(s(s(z)))))),
% 3.14/3.31 inference(modus_ponens,[status(thm)],[14149, 14148])).
% 3.14/3.31 tff(14151,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14150, 171, 14004, 1, 9835, 14092, 10693, 14144])).
% 3.14/3.31 tff(14152,plain,(~b(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14153,plain,
% 3.14/3.31 (r(s(s(z)), z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[157, 14152])).
% 3.14/3.31 tff(14154,plain,
% 3.14/3.31 (~b(z, s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[13976, 96, 14044, 14153])).
% 3.14/3.31 tff(14155,plain,
% 3.14/3.31 (r(z, s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[293, 14154])).
% 3.14/3.31 tff(14156,plain,
% 3.14/3.31 (~r(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14030, 96])).
% 3.14/3.31 tff(14157,plain,
% 3.14/3.31 (b(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[550, 14156])).
% 3.14/3.31 tff(14158,plain,
% 3.14/3.31 (~b(z, s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14037, 14157])).
% 3.14/3.31 tff(14159,plain,
% 3.14/3.31 (r(z, s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[124, 14158])).
% 3.14/3.31 tff(14160,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14064, 14157, 14044])).
% 3.14/3.31 tff(14161,plain,
% 3.14/3.31 (r(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[9958, 14160])).
% 3.14/3.31 tff(14162,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[6247, 14161, 14159, 14153, 14155])).
% 3.14/3.31 tff(14163,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14164,plain,
% 3.14/3.31 (b(z, s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[93, 14163])).
% 3.14/3.31 tff(14165,plain,
% 3.14/3.31 (~r(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14030, 11727])).
% 3.14/3.31 tff(14166,plain,
% 3.14/3.31 (b(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[550, 14165])).
% 3.14/3.31 tff(14167,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14064, 14166, 14044])).
% 3.14/3.31 tff(14168,plain,
% 3.14/3.31 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[11942, 14166, 14044, 14153, 4])).
% 3.14/3.31 tff(14169,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[9958, 14168, 14167])).
% 3.14/3.31 tff(14170,plain,(~b(s(s(s(s(s(z))))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14171,plain,
% 3.14/3.31 (r(s(s(s(s(s(z))))), s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[479, 14170])).
% 3.14/3.31 tff(14172,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14012, 14164])).
% 3.14/3.31 tff(14173,plain,
% 3.14/3.31 (r(s(s(s(s(z)))), s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[9955, 14172])).
% 3.14/3.31 tff(14174,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14045, 83, 14044])).
% 3.14/3.31 tff(14175,plain,
% 3.14/3.31 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[3668, 14174])).
% 3.14/3.31 tff(14176,plain,
% 3.14/3.31 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[13768, 14175, 14171])).
% 3.14/3.31 tff(14177,plain,
% 3.14/3.31 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[1368, 14176])).
% 3.14/3.31 tff(14178,plain,
% 3.14/3.31 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[11961, 14177, 14044, 14175])).
% 3.14/3.31 tff(14179,plain,
% 3.14/3.31 (b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[2614, 14178])).
% 3.14/3.31 tff(14180,plain,
% 3.14/3.31 (~b(s(s(s(s(s(z))))), z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14052, 14164])).
% 3.14/3.31 tff(14181,plain,
% 3.14/3.31 (r(s(s(s(s(s(z))))), z)),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[145, 14180])).
% 3.14/3.31 tff(14182,plain,
% 3.14/3.31 (~b(s(s(s(z))), s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14017, 14164])).
% 3.14/3.31 tff(14183,plain,
% 3.14/3.31 (r(s(s(s(z))), s(z))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[1173, 14182])).
% 3.14/3.31 tff(14184,plain,
% 3.14/3.31 (~r(z, s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[10522, 14177, 14183, 14181])).
% 3.14/3.31 tff(14185,plain,
% 3.14/3.31 (b(z, s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[9192, 14184])).
% 3.14/3.31 tff(14186,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14057, 14185, 14179, 14044, 14164, 83])).
% 3.14/3.31 tff(14187,plain,(~b(s(s(s(s(s(z))))), s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.14/3.31 tff(14188,plain,
% 3.14/3.31 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[427, 14187])).
% 3.14/3.31 tff(14189,plain,
% 3.14/3.31 (~r(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[7054, 14188, 14171, 14173])).
% 3.14/3.31 tff(14190,plain,
% 3.14/3.31 (b(s(z), s(s(z)))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[550, 14189])).
% 3.14/3.31 tff(14191,plain,
% 3.14/3.31 ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[11210, 14004])).
% 3.14/3.31 tff(14192,plain,
% 3.14/3.31 (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14191, 14190, 14171, 14164])).
% 3.14/3.31 tff(14193,plain,
% 3.14/3.31 (r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[3668, 14192])).
% 3.14/3.31 tff(14194,plain,
% 3.14/3.31 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[13768, 14193, 14171])).
% 3.14/3.31 tff(14195,plain,
% 3.14/3.31 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[1368, 14194])).
% 3.14/3.31 tff(14196,plain,
% 3.14/3.31 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[11961, 14195, 14044, 14193])).
% 3.14/3.31 tff(14197,plain,
% 3.14/3.31 (~b(s(s(s(z))), s(s(s(s(s(z))))))),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[14106, 14195, 14188, 14173])).
% 3.14/3.31 tff(14198,plain,
% 3.14/3.31 ($false),
% 3.14/3.31 inference(unit_resolution,[status(thm)],[2614, 14197, 14196])).
% 3.14/3.31 % SZS output end Proof
% 3.14/3.32 % E exiting
%------------------------------------------------------------------------------